The First Amendment has always applied to private property "town squares" that are open to public, originally this was decided in the case of indoor shopping malls.
I think/hope there would be raised eyebrows if government agencies set up shop in private malls. Malls have realistic alternatives. Twitter doesn't, even for some government services.
If you're thinking of Pruneyard v Robbins, that only applies in CA. And that wasn't based on the 1st Amendment, but on California's own constitution.