But twitter is working with the government in hosting the tweets and thus assumes responsibility to provide a public square
No. No it doesn't. Allowing the government to use your service does not thereby make it part of the government.
No. No it doesn't. Allowing the government to use your service does not thereby make it part of the government.
(Nitpick: "free speech" is a general philosophical concept; we're talking about the 1st Amendment, which is a particular application of one of many views on that concept)