Could starlink be a way to maintain global connectivity in the face of government control? Would they try to jam satellite connections?

It's harder to jam Starlink than GPS because the signals are directional, but if a government doesn't want you using it, they can just make the dishes illegal and throw you in prison for having one.

Starlink is under USA jusrisdiction, as far as I know. I'm pretty sure there's no concept of "international waters" for communication satellites.

AFAIK Most of the traffic goes: subscriber <-> (single) satellite <-> local base station. And the latter operates under the rules of given country.