I don't think the First Amendment would ever require the government to host private speech. The rule is basically that if you host private speech, you can't discriminate by viewpoint (and you're limited in your ability to discriminate by content). Even so, you can always regulate time, place, and manner in a content-neutral way.

The easiest way to do it is to simply do one of the suggestions of the linked article, and only permit government users and government servers to federate inbound, so that the government hosted servers never have to host anything private, while still fulfilling the general purpose of publishing public government communications, for everyone else to host and republish on their own servers if they so choose.

Yeah, I don't have a complete answer here. I think that Terms of Service requiring standards of behavior are quite reasonable - people in Congress, for example, are required to conduct themselves to a certain standard or be ejected. Same goes for courtrooms.

There may be a "minimum threshold" for content or communities that are blocked, on the basis of materials provided (hate speech, harassment campaigns, doxxing, CSAM), but I'll readily admit that this is conjecture.