Part One: Preventing Competititon.
I note that a galactic emperor could pevent ambitious governers or kings of kings of kings or other subordinates from building more expensive or impressive palaces by regulations or laws. Or possibly by paying governors and vasal kings fixed salaries and and forbidding them from spending tax money on their palaces. Or by spending an amount of taxes fixed by law with penalties for exceeding.
Or maybe the imperial government would manufacture prefabricated palaces to a regulan design for proconsuls and kings of kings and ship them out to the planets to be assembled.
So you galactic empror wouldn't have to worry about his subordinates equalling or surpassing his palace if he coud prevent them from trying.
Of course, independent kings of unconquered planets, and star systems, and rivals for the title of galactic empire ruling similarly large numbers of star systems could build palaces to rival your emperor's palace.
Part two: Do Your Palace Research Before Writing.
One thing which a witer could think about when designing the palace of a galactic emperor is reading about other fictional palaces in fantasy and science fiction.
Of course some writers even of fantasy and science fiction suffer from a lack of imagination in designing impressive palaces.
I remember in one of Poul Anderson's King of Ys fantasy novels the protagonist met with the real Roman Emperor Magnus Maximus (reigned 383-385) in the imperial palace at Trier. And the room was described merely as a "splendid throne room". And I had to think that either Anderson didn't do his research, or he was "damning with faint praise" the throne room in the imperial palace at Trier, by callig it merely "splendid".
In The Worm Ourobos, by E. R. Eddison, Chapter One "the Castle of Lord Juss":
She spoke, and the first low beams of the sun smote javelin-like through the
eastern windows, and the freshness of morning breathed and shimmered in that
lofty chamber, chasing the blue and dusky shades of departed night to the corners
and recesses, and to the rafters of the vaulted roof. Surely no potentate of earth, not Croesus, not the great King, not Minos in his royal palace in Crete, not all the Pharaohs, not Queen Semiramis, nor all the Kings of Babylon and Nineveh had ever a throne room to compare in glory with that high presence chamber of the lords of Demonland.
And the presence chamber does have an impressive design. Though Eddison is unclear in some details of the description, such as writing about "rafters of the vaulted roof".
As I said, the presence chamber is impressively designed, but the only thing about it which has never been equalled and surpassed on Earth in real history is:
But a great wonder of this chamber, and a marvel to behold, was how the capital of
every one of the four-and-twenty pillars was hewn from a single precious stone,
carved by the hand of some sculptor of long ago into the living form of a monster:
here was a harpy with screaming mouth, so wondrously cut in ochre-tinted jade it
was a marvel to hear no scream from her: here in wine-yellow topaz a flying firedrake: there a cockatrice made of a single ruby: there a star sapphire the colour of
moonlight, cut for a cyclops, so that the rays of the star trembled from his single
eye: salamanders, mermaids, chimaeras, wild men o' the woods, leviathans, all
hewn from faultless gems, thrice the bulk of a big man's body, velvet-dark
sapphires, crystolite, beryl, amethyst, and the yellow zircon that is like transparent gold.
And the only thing impressive about those jewel capitals is the vast size of the original gems they were carved out of, unavailable on Earth. And I for one am not impressed merely because the builders had access to larger amounts of rare minerals than on Earth. That is a feature of the location, the result of luck instead of personal effort, and not a virture of the architectural skill of the designers.
The banqueting hall in the castle of Carce later in the book, by contrast, is rather sinister looking, but it achieves its strong effect through architectural design instead of rare materials. And I think that later on there is a chamber built by the gods that is even more impressive.
And in a future society people should be able to make gems at least as large as the gems in the presence chamber, whenever they want to, and so it would not be expecially impressive for a galactic emperor to use gems of that size. Of course if the Emperor synthasizes germs billions of times larger than anyone else has ever synthsized in order to carve verious parts of his palace out of those vast gems, that may be impressive.
And you may remember seeing the movie Excalibur, 1981, in which the castle of Camelot appears to be made of blocks of solid gold. And to me that merely shows how dumb Arthur is in this movie, using gold in solid blocks as construction material, to build a castle with an architectural design that is not nearly as beautiful in shape as some real castles on Earth, instead of using thin sheets of gold as surfaces on the walls, as gold should be used. What form of decoration can be more spendid than gold and glass mosaics, for example?
So I think that the emperor would be a little silly to obsesse about using expensive materials in his palace, instead of considering the size and the architectural design of his palace as the most desirable features for those who live in it, and the most impressive to those who see it.
I also note a failure of research on Eddison's part when he lists the palaces on Earth which are suprassed by the presence hall in the castle of Lord Juss:
Surely no potentate of earth, not Croesus, not the great King, not Minos in his royal palace in Crete, not all the Pharaohs, not Queen Semiramis, nor all the Kings of Babylon and Nineveh had ever a throne room to compare in glory with that high presence chamber of the lords of Demonland.
And I think that all the really great palaces on Earth were built after the ones he mentions, though before the ones listed at:
I am thinking of Nero's Golden House, the Flavian Palace built by Domitian, Hadrian's Villa at Tivoli, Constantine's palace at Trier, Germany, the Palace of Galerius at Thessalonika, the Great Palace at Constantinople, the Blachernae Palace at Constantinople, The White Palace at Ctesiphon, the Arch of Chosroes at Ctesiphon, The Round City of Baghdad, the Abbasid palaces at Samarra, etc.
Part Three: Who'll Stop the Rain? And Why Stop the Rain?
As an example of a science fiction writer's lack of imagination, in James Blish's Mission to the Heart Stars, 1965, the characters from Earth go to the capital planet of the Hegemon of Malis, ruler of the galaxy. When they enter the vast throne room, one of the characters wonders whether the throne room has it own weather and rain inside. And Blish describes it as a whimsical thought.
Here is a link to a list of buildings with the largest interior volumes on Earth:
My answer to https://worldbuilding.stackexchange.com/questions/153965/how-not-to-turn-volkshalle-into-a-rain-factory indicates that some of the buildings on the list do have interior mist, clouds, and rain.
So by having a character merely get carried away by their imagination and exaggeratedly wonder if the room was big enough to have internal weather, Blish was suggesting that a galactic emperor might possibly have had such a modest and humble throne hall that it was actually even tinier than the Vehicle Assembly Building and other buildings on that list!
And unlike the asker of the question, I think that interior rain can be a feature, and not a bug, of the design.
Maybe a galactic emperor's throne room would be large enough to have interior rain, and the interior weather would be controlled by technology so that it rained, and thundered at the right moments to emphasise the words of the galactic emperor, sort of the effect that Chosroes or Khosrow II imitated on a much smaller scale in his fabulous palace or temple building.
Part Four: What is Art? And Which is the Most Impressive Art?
So I think that the effect of a galactic emperor's palace should depend a lot on it's size, far vaster than anything ever built on Earth, and on the splendor and beauty of its architectural design, rather than the expense of its construction materials. Of course the materials used on the surfaces of the exteror and interior of the palace can be very expensive materials, if they are also very beautiful materials.
I mentioned above gold and glass mosaics. Gold is expensive, even when used in thin sheets, and glass used to be expensive enough to be used in fine jewelry instead of costume jewels. And of course the colored glass cubes in wall and ceiling mosaics can be be repaced by cut and faceted jewels to make the mosaices even more expensive and beautiful - in fact, jewels have occassionally be used in mosaics.
If your palace has countless millions of square meters of walls and ceilings covered with mosaics designed by brilliant artists and made out of gazillions of jewels, that will be expensive both in materials and artistry, and will be very impessive and beautiful.
Another answer suggested that a palace could be filled with the greatest works of art from over the galaxy, and thus be a vast museum. But paintings, and rugs, and tapestries, and sculputures, are comparatively small and movable items, and are not exactly features of the building which they happen to be displayed in at the moment.
And one of the greatest arts is architecture. So the Philadelphia Museaum of Art has a wing dedicated to displays of architecture, with rooms from various places and eras on display. And possibly the imperial palace could contain original or duplicate rooms designed by all the greatest architects from thousands of planets and millennia of history.
Of course if the rooms in the palace are large enough, each can contain exact full scale replicas of famous works of architecture - or possibly the original buildings - from all the planets of the Empire. Or maybe even exact full scale replicas of famous cities in the empire.
And possibly, if the rooms in the palace are large enough, they can also contain famous vehicles, like cars, trains, tanks, construction equipement, ships, submarines, airplanes, space vehicles, etc., from the history of thousands of planets and star systems.
As I wrote above, arcitecture is often considered one of the greatest arts, and architecture often integrates painting and scupture, two of the other greatest arts, into its design. So by making each room in the palace a masterpiece of architecture and interior decoration, each room can be a gigantic and non portable work of art. And if some of that interior decoration is metal and glass mosaics, and perhaps using cut and faceted jewels for some or all mosaic parts, the interior artwork can be dazzling.
And such glittering mosaics can be used on the exteriors of buildings. I used to walk past a building in Philadelphia at the right time of day for the gold colored metal in the mosaic around the door to reflect the sunlight down to me. I have read that part of the facade of the Baths of Caracalla in Rome was decorated with silver and glass mosaics.
One facade of Nero's Golden House was said to be decorated with gold and gems.
Part Five: Architectural Design.
And here are just a few very brief suggestions about the architectural design of a galactic emperor's palace.
If you Google for At The Court of King Arthur by Samuel E. Lowe, and search for images, a picture of the blue and white endpapers of one edition is like to be one of the results. On the right side is a knight on a rearing charger, and on the left there is a fairy tale palace to end all fairy tale palaces. Ever since i was a child, I have considered that to be the fairy tale palace design to strive to equal and surpass.
And you should look at the floor plan of the Villa Romana del Casale:
Aand the floor plan of the ruins identified as the Palace of Antiochos in Constantinople:
Those are good examples of ways in which the floor plan of a palace could differ from those of ordinary buildings, as it should.
And to me the absolute best floor plan would be one which is made of radially symmetrical elements which are combined to make radially symmetrical units which are turn are parts of larger radially symmetrical units which in turn are parts of larger radially symmetical units, and so on and so on.
Part Six: Sufficiently Advanced Technology.
Also the palace of a galactic emperor should use various advanced technologies.
Suppose that a galactic emperor built a super expensive palace, and then some historian pointed out that it lacks a technologically advanced feature which was used by some ancient emperor on Earth, and thus the modern palace could be considered less technologically advanced than a palace built millennia earlier by a much les advanced society. I think that the Galactic Emperor would feel humiliated, and thus his architects might feel tormented - by the imperial torturers.