Free speech the value is about the government. Free speech is always about the government.

It's true that some people think this. Other people think the 1st Amendment exists for a reason less simplistic than "a government shouldn't censor people," something to do with a healthy human society: https://theintercept.com/2014/08/21/twitter-facebook-executi...

This is not to argue that the 1st Amendment should compel anything beyond protection from government censorship, but that the value it exists to promote applies to wider situations

Is it? Do you have sources to back that up? In principle it seems like it's a concept that could apply equally to freedom from retribution from one's family/local community/internet service provider.