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.
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.
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.
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.