What about seaweed? The sargasso sea acts as a breakwater. So mass - when light individual objects distributed over a broad area - can act to dampen waves.
This is good out of the box thinking, but I’d take it a step further than you did.
Why not design a floating city around the very idea of seaweed aquaculture and plastics recycling, and site it in the middle of an oceanic gyre? You could build a floating kelp raft network a mile across, and put your habitable area in the middle of it. The kelp would effectively act as a mile wide series drogue.
That also gives you another element nobody’s talking about, at least in this thread anyway … sustainable economics. You have an export crop baked into the concept.
I see I should have read further down.
Crapping on the seaweed farm idea is just as dumb as crapping on the idea of a corn farm because you don’t like corn. You grow corn and sell it and buy whatever you need. That’s how economies work. Without a resource to sell, your entire floating city is just going to be a tourist destination, nothing more.
Instead of looking for a place shallow enough to grow kelp, just sink some long concrete beams off of some floats and grow the kelp on that. Build that into a subsurface hex grid network on pivots, with floats at each of the vertexes of the hex grid, and cultivate kelp on each of the beams. The whole thing undulates in the water, deadens any wave or swell action, and you tie your central living space into the grid. If you site it in the middle of a gyre, it pretty much stays put in the same region we’re collecting plastics trash now, without the need for an anchor - or at least a severe one - because there’s nothing nearby to bump into. If it gets moved by a storm, move it back when the storm is done with some light anchor lines that you pay out during the storm, or with propulsion.
Even if you don’t use all the kelp for aquaculture, it still gives you the breakwater.
And you can use algae as shrimp feed. (as well as some of your sanitary waste) Everybody likes shrimp.
Throw in a plastics recycling operation in the central habitated area to create hydrocarbon fuels for use by the city, while also cleaning the ocean.
That’s the idea. It has a lot of the problems tied up in one neat little bow.
You could fuel the whole city off of methane and sell ethanol to passing boats.