I know very well the 1st Amendment applies only to the State - my whole series of posts is about the problems that arise due to that. Free speech as a concept is not limited to the 1st Amendment.
Your right to make noise with your pie hole in no way obligates anyone else to listen to, or even hear you, let alone broadcast that noise to a larger audience than you would have had without their help. Full stop.
There is absolutely a legitimate, and very, very important conversation to be had around whether, e.g., online censorship or moderation or "deplatforming", or whatever, might constitute something functionally akin to prior restraint, where the edge cases are in those questions, and what to do about all that.
That said, having those discussions about private behavior using terms that are — and historically have more or less always been — used in the specific context of the State only confuses things.
My point being: if we're going to have that discussion, which we for reals should be doing, let's try to do it in a way that doesn't make it harder to have, let alone have productively.
The attempt to expand the specifically and narrowly constrained notion of "Free Speech" (note the capitalization) to domains other than a constraint upon the State is a specious conflation, and ultimately yields more heat than light.
EDIT: I mean, really, how productively can that conversation be had if it's using terminology that enables randos who don't meaningfully understand this distinction to pile on, all, "But the Twitters violated my 1st Amendmentses!"?