But the absolute freedom of speech is just from prosecution of the government (correct me if I am wrong). private parties can always deny you their platform to be used for hatemongering or anything else really.
The first amendment is scoped to the government because the constitution is scoped to the government.
Yes and no. It's true that he Constitution is scoped to government, so if there was a free speech principle that was not it might have been limited in the Constitution.
But the free speech principle actually underlying the Constitutional text is also scoped to government in that involves and relies on the freedom of all actors except government to choose what speech to make, endorse, support, relay, or associate themselves with to promote the competition of ideas and the success of good ones and elimination of bad ones, on the concept that the former will be more likely to be relayed and the latter will die out from failure to convince people to participate in spreading them.
If platforms of overwhelming reach and intrusiveness actively relay content blindly, it makes it much harder for the winnowing process to work.