As mentioned above, natural light would be a serious concern. Here is a graph of the penetration of different natural light colors:
Below fifty meters in muddy, stirred-up coastal environments you will be living in night-time level darkness. Assuming this is an active city, they will need to seriously manage silt and dirt circulation to improve underwater visibility.
Thankfully, the size of an underwater continental shelf can be quite large. Look at the portion in the Pacific. Even if there were only scattered continental shelves like this, there could still be 2-20% of the world habitable with complex ocean city-building technologies. That is more than enough space for a vast civilization.
The civilization would likely focus first on expanding out the existing atolls and other land as far as possible. They could create artificial islands through dredging, underwater mining, and massive infrastructure projects. However, at some point it would be more economically feasible to build up from the seafloor, rather than raising the seafloor itself. Large engineered platforms for stone from the ocean floor could be built up in 50 meter high platforms for each building. The buildings would then have their tops emerge into the sunlight above. 87
Causeways and other over-water bridges would connect the massive building-structures.
The underwater portion would still be useful, especially close to the surface. These could have windows and still receive light. Further down, by about 50 meters, and you are essentially "underground". Think about current underground infrastructure, and you have an idea of what you can have situated at these depths-- industry, storage, communications, less desirable habitations, processing, mining, ect.
There could also be underwater tunnels running between the bottoms of these buildings. It would be somewhat more economically feasible to build above-ground, and yet underwater tunnels, rather than simply carving through solid rock below the oceans.
So, you would have well-developed atolls, surrounded by huge expanses of continental shelf with buildings rising from the seafloor, connected by roads and causeways, with underwater structures connected by oceanfloor covered roadways and tunnels.
Agriculture, of course, would focus on fishing , seaweed farming (whatever local biological equivalent) and perhaps creation of giant algae mats, which can be processed for multiple nutrients. Perhaps some local woody substance could be harvested, dried, and burned for heat.
For a century or two they could exhaust carbon-heavy deposits for energy production (oil equivalents) before running out. Of course the opportunities for wind power are enormous. Floating solar panels might cover significant portions of the more "open sea" portion of the world. This would disrupt local wildlife, presumably, so there would be concerns by conservationists and environmentalists.
All in all, yes, there are some real possibilities for your ocean metropolis. It is not the most efficient world to settle, but it is does sound like an interesting and beautiful one. 87