The new age of sail is electric motors coupled with a solar array and batteries. While each boat is docked they can buy or sell power to the main floating unit. I think it would be easier to build a floating island if the entire thing was modular. Scale-able in a way that allows the city to expand with new habitants.
Very simply put, it could be a floating dock with the capacity to add more platforms when needed. Each slip in the dock would be interchangeable with a standard power, water and sewage connections. Individuals would buy floating homes (boats) with the standard connection and be able to sign a lease and be part of the community. Other essential facilities can still be modular. A restaurant or farm platform or whatever needed could be connected in the same way.
Using a strategy like this would offset much of the upfront cost of building an entire island community. It also allows the community to grow and change easily.