Then have a rule that the any elected member of the current house(s) can have an account. Moderation actions on those members should be rare, public, and conducted on the authority of the Speaker (or sensible equivalent for the political system). Whether the posts should enjoy parliamentary privilege, and/or be constrained by the rules of "unparliamentary language", is a detail that would need working out

Of course this has the downside of losing your account if you lose your seat, and not getting one until you're elected, but hopefully this will nudge political parties to run their own instances for their members

The above would presumably not apply to other accounts like the press accounts of a government department. I think they/the acting government can police themselves, as they currently do with Twitter, and as they've done with statements to the press since before computers