Suppose USGOV takes over Facebook, then is it bound by 1A for all users? Or just those in US jurisdictions?

You'd surely need it to be taken over by a supra-national body like the UN, given it has a supra-national user base.

Not really. As the owner of a site, the government controls its own speech and is not under any obligation to show “both sides” of an argument. Sure, it can’t only show your comment vs mine, but it can definitely choose which propaganda to spread.

Exactly. As long as Facebook is a private corporation, the First Amendment protects their right to arbitrarily censor the speech on their platform however they wish.

The way state-controlled media censorship has turned out in other countries is well-known, but having our public spaces controlled by a patsy of the government, who is not subject to the same restrictions as the government even in theory, is not a better outcome.