Like, if a community really wanted a unicycle repair shop, how would that get started?

Pretty much the same way a community would start a co-op right now.

Would that be up to a local government (or some other governing body)?

Public participation, of course. The community would form councils, where people would collectively decide whether this is a good idea or not. That literally what the word soviet means - councils of people making decisions (which is why the Bolsheviks hijacked them and turned the word into a cruel joke).