A few comments.
Why do you assume that a galactic emperor would be evil?
I say that the president or monarch of an independent sovereign planetary state, star system, state, or species state, would be evil, because the function of independent sovereign states to occasionally make war against other sovereign independent states. Fighting wars and making their own citizens - just as much as the citizens of other realms - experience horror and suffering, destruction and death, is the function of independent governments.
And in a society with rapid interstellar travel, independents would have the power to devastate enemy planets and kill all their inhabitants, which is trivially easy compared to having rapid interstellar space.
So no matter how evil a galactic emperor might be as a person, their regime would be saintly compared to any independent sovereign state ruling only part of the known galaxy.
I note that most countries in the world today have various administrative divisions with varying powers, and that the main function of such administrative divisions is to do things which are good for the people within them. So most administrative divisions manage to do things which are good for the people within them without being independent sovereign countries with the power to fight wars and kill people.
Being a resident of an administrative division within a larger administrative division within a larger administrative division within a larger administrative division within a larger administrative division and so on up to being part of a galactic empire is much safer than being a resident of a sovereign independent state surrounded by other sovereign states with the power to make war against them.
So don't go calling galactic emperors evil.
You write that a planet as the location of a Galactic emperor's palace would have this disadvantage:
and also cannot dodge any relativistic projectiles launched through the interstellar wormhole network by an aspiring rebellion.
Any planet available for a galactic emperor to build a palace on would either be part of a star system or else be a rogue planet in interstellar space.
A planet in a star system would move constantly, orbiting around a star or a pair of stars.
A rogue planet in interstellar space would move constantly, orbiting around the center of the galaxy.
Even a rogue planet in intergalactic space would move constantly, since it would have formed within a star system within a young star cluster within a galaxy, and must have been given sufficient speed by gravitational interactions to escape from its star system, its cluster, and its galaxy.
So if the mouths of wormholes are fixed in space, the palace planet, like every other planet, would be constantly moving relative to the mouths of the nearest wormholes.
So if a projectile is sent at relativistic speeds through the wormhole, its trajectory will have to be properly aimed and adjusted on the far side of the wormhole.
And considering that the two mouths of the wormhole should be light years apart, a projectile sent through the two mouths should have only a very narrow range of possible trajectories.
So it seems to me that it would be extremely rare for the palace planet, or any other planet, to be within such a thin and narrow cone of possible trajectories of relativistic projectiles emerging from a wormhole mouth. I would say that the odds against a projectile emerging from a wormhole mouth and striking a planet even once in galactic history would be astronomical.
And that is assuming that the wormhole network is natural. If it is artificial and the galactic empire created it, the wormhole mouths would be planned to be located where they didn't point toward inhabited planets.
What if the wormhole mouths are attached to star systems and move with the star systems?
That way the wormhole mouth could be located a lot closer to the palace planet, making travel times shorter, and increasing the probability that the palace planet could be struck by an unsteerable relativistic projectile emerging from the wormhole mouth.
But when you start with astronomically low odds that something would happen, and then increase them millions of times, the odds will still be astronomically low.
The obvious way to attach the mouth of a wormhole to a star system would be with gravity. The wormhole mouth might be generated by enormous machines which would have mass and gravity. The wormhole mouth itself might have mass even without generating machines.
So the wormhole mouth, having mass, and being (relatively) near a star, would orbit around that star, just like the palace planet in this case.
Assume there is a carnival carousel surrounded by a circular racetrack. Suppose a loaded gun is lying on the floor of the carousel, pointed outwards toward the race track. Suppose that the carousel is turning, and cars are racing in the racetrack, when the gun goes off and shots toward the racetrack. Wouldn't the odds against hitting the bullet from the gun hitting one of the racecars be very large?
Suppose that there is a line directly from the center of the Sun to the center of the Earth. If that line is extended outwards into space it will pass the orbits of the other planets in our solar system. But considering how small a planet is compared to the total circumference of its orbit, that line will have a very low probability of going through a planet at any one time.
And in fact that line will probably not intersect the orbit of any outer planet at all, let alone while that the line from Earth and the planet occupy the same spot in the orbit.
The orbits of all the planets are tilted slightly compared to the orbits of the other planets. So by the time a line from Earth in the plane of Earth's orbits passes tens of millions or hundred of millions of miles outward, it will pass "above" or "below" the plane of the other planet, by a distance much greater than the width of the planet.
So if a slight tilt is enough to make a line from the Earth miss the orbit of another planet, the creators of the wormhole network can give the wormhole mouths orbits which are tilted much more, to increase how much a line from the wormhole mouth will miss the orbits of the planets.
And of course the creators of the wormhole network can give the wormhole mouth an orbit outside of the orbit of the palace planet or any other inhabited planet. And if the wormhole mouth only opens in the direction facing outward from the star, any relativistic projectile emerging from the wormhole mouth will only be able to travel away from the inhabited planet, not toward.
Maybe a projectile can emerge in any direction from the wormhole mouth.
In that case any gigantic space habitat palace or palace on a planet would be defended like a major planet in E.E. Smith's Lensman series of space operas would be defended.
In the series, the two sides learned how to create artificial hyperspatial tubes leading to any destination, much like artificial wormholes, and so could suddenly create many hyperspatial tubes leading to an enemy world and send invasion fleets with millions of space battleships through them to attack.
They would also send major weapons thought the hyperspatial tubes, not mere fleets of millions of space battleships. They attached giant engines to planets and tried to crash them into target planets. They built planet-sized negaspheres, balls of negative matter that cancelled out normal matter, attached giant motors, and tried to smash them into target planets.
So any planet which was expecting to be attacked would have major defenses such as fleets of millions of space battleships, and giant orbital fortresses, and a bunch of planets and negaspheres with with giant engines ready to smash into attacking planets and negaspheres and knock them off course.
And by the last battles in the series really powerful offensive and defensive weapons were developed.
So I think that any really powerful galactic emperor would have really powerful defenses in place to defend the various star systems where their various palaces were in giant space habitats and/or on planets.
So they could attach space drive engines to asteroids and place a line of asteroids in front of the wormhole mouth in the the system. A spaceship on a normal slow approach would be traveling slowly enough to have time to swerve and avoid the first asteroid, but a relativistic projectile would smash into the first asteroid in line causing a gigantic explosion. Then the next asteroid would be moved forward to plug up the gap in front of the wormhole mouth.
Suppose that the wormhole mouth is a spherical shape and objects can exit it in any direction.
Then the thing to do would be to put many concentric spherical shells around the wormhole mouth, each shell consisting of equally spaced pebbles or grains of dust. If an object came out of the wormhole mouth at a relativistic speed, it would run into pebbles or even dust with enough force to explode.
No doubt there could be cylinders running though each concentric shell of pebbles or dust, the interiors of the cylinders clear of pebbles or dust so spaceships could pass through them. But each cylinder would have great doors at each end and and a spaceship would have to stop in front of a cylinder to be checked out before the doors would open and let it through, and any object which rammed a cylinder would be destroyed.
And of course there could be space battleships and gigantic battle stations, etc. posted around the wormhole mouth to destroy any hostile missiles or ships which may emerge from it.
And possibly there are many lifeboats/escape capsules throughout the palace; if an alarm is sounded people in the palace can rush into the escape capsules and zoom away from the palace and the planet or space habitat, and take refuge with the battle fleet.
So it seems to me that it would be possible for any system which contained a palace on a planet or in a gigantic space habitat to be well guarded against attacks.
And possibly the galactic emperor could have several different palaces in systems tens of light years apart, and travel between them in gigantic palatial spaceships guarded by vast fleets of space battleships.
While writing this, I had a thought.
There is a legend that King Louis XI of France, fearing assassination, slept in a different room each night.
I don't know how many different bedrooms he had to choose from at his favorite residence, Chateau de Plessis-lez-tours. 365, one for every day of the year? Probably not that many. About 30, one of every day in a month? Maybe. 7, one for each day of the week? He should have had at least that many. And no doubt he didn't sleep in the same order time after time, or hypothetical assassins could predict where he would seep each night.
And legend claims that Ch'in Shih Huang Ti, or Qin Shi Huangdi, the First Emperor of China, built a ring of palaces around his capital city, connected by underground passages so nobody could see his coming or going, and slept in a different palace and room each night. As I remember, there were supposedly over 100 or even over 200 of those palaces, so not enough for every day in the year, but enough to go for months without repeating.
And considering how many times, almost infinitely, more powerful a galactic emperor ruling a highly technologically advanced society would be compared to Louis XI or even Qin Shi Huangdi, a galactic emperor could do something almost infinitely greater than that.
If you go to the PlanetPlanet blog, and the section called Ultimate Solar System, you will find blogs dedicated to designing fictional solar systems with as many habitable planets as is scientifically possible.
In "The Ultimate Engineered Solar System" there is a design for a solar system with literally hundreds of potentially habitable planets in its circumstellar habitable zone.
Though of course the author admits that even though such a solar system could exist and all the hundreds of habitable planets could have long term stable orbits, it would seem to be statistically impossible for such a solar system to form naturally, and so it would have to be engineered, created by a highly advanced civilization which built planets and/or moved them into the correct orbits.
So so possibly the civilization in your story found such a multiplanet system left behind by a past advanced civilization. Or possibly it is advanced enough to build one themselves.
And I don't know how many days there are in a year in the calendar used by your civilization, but I guess that a system with hundreds of habitable planets could have one planet for each day of the year in its calendar.
And possibly the emperor sleeps in a different bedroom in a different palace on a different planet in that system each night.
See the answers to https://worldbuilding.stackexchange.com/questions/186407/the-emperors-new-palace
Especially my answer.