Viability of underwater palace built by merfolk

Question

In my fantasy setting there are merfolk who live deep under the ocean and neighboring human civilizations nearby based on iron age civilizations like the ancient greeks and phoenicians.

I would want to know what would be necessary to allow the merfolk to construct and maintain a palace underwater. The palace would be the same size as contemporary human-built palaces, which is during the 500s b.c. The merpeople can easily obtain building materials from humans as part of trade, and some can magically control coral to change its shape and cause it to rapidly grow.

They have hands with webbed fingers and roughly human-level dexterity.

Answer 1

The merpeople can easily obtain building materials from humans

A.

The Romans had underwater concrete

More than 2000 years ago, the Roman Empire invented a unique marine concrete that allowed for the construction of enormous, durable structures – even underwater. Incredibly, the exact chemical properties of this concrete mixture have eluded scientists to this day – but now, researchers from the University of Utah believe they may have finally cracked the code. Scientists Uncover the Chemical Secret Behind Roman Self-Healing Underwater Concrete

The Roman scholar Pliny the Elder described underwater concrete structures that become “a single stone mass, impregnable to the waves and every day stronger.” Seawater is the secret to long-lasting Roman concrete

B.

Pre-fabricated stonework

Humans can sink pre-shaped stonework as directed. All the Mers have to do is assemble the building. Gravity will hold everything together - there are no storms or strong currents on the deep sea bed.

Answer 2

You have intelligent traders, who live and work underwater. Those are by far the largest hurdles to large scale underwater construction.

Once cities exist...

Old cities formed at cross roads close to resources. Food being one of the more critical resources. Once you have cities you will have some group wanting to show how awesome they are with a big building. Could be a church, palace, something honoring the gods, or some combination. Once they are building cities somebody will get the idea in their head to build BIG.

Where

So merfolk cities will form along trade routes. Primary route would be the surface of the seas/oceans, due to lower friction. Shallow so they don't have to waste time dealing with slow ascents to avoid bends. Shallow tends also to be close to land and thus land trade routes.

Cities need food, but cities don't move, plants don't swim away, so areas that are surface lit. So again shallow areas. Ideally with high nutrient for good plant growth. But away from the down stream of other large cities to avoid water pollution.

Material trade?

Stone is heavy so it will not be transported far from the quarry. Initial cities would probably be built with stone the was found loose or stone that could be pried out with leavers.

Later cities would probably source from near shore quarries. Where metal tools traded from land people could be used more effectively in air. Rock loaded onto boats/barges then moved to nearly above the construction site and offloaded overboard into the water.

Metal tools would be a major trade item from land fold to merfolk. Certain decorative woods, ceramics, would also be trade items.

Conclusion.

Again. Once you have water breathing intelligent traders, cities will form. Once cities form, big buildings will be built. Weather those buildings are local gods or the local lords will be dependent on the culture.

So yes, underwater merfolk palaces are plausible.