Government-built doesnt necessarily mean government-run or government moderated.

You could, e.g., have funding for social media "rails", as in developing fediverse platforms of various sorts as public goods on which people could build commercial, community or personal instances.

There is nothing unusual in such arrangements and the funds required are miniscule compared to other government funded infrastructures.

This would provide an enormous range of possibilities. In would not by it self "solve" the various frictions that we know plague online platforms