You ask three different questions here but expect only one response.

You don’t police the English language. I don’t know what else to tell you.

One phrase can refer to multiple things; “free speech” often refers to the ability to say whatever you like* without repurcussions from an authoritative figure, be that the government, Elon Musk’s cronies, or Lemmy moderators. Obviously it is not a constitutionally protected right in the latter contexts, but then again the phrase wasn’t “right to free speech.”

You cannot claim this on behalf of other people. I myself sometimes refer to lax moderation rules as “free speech focused” moderation. It has nothing to do with the government.

That isn’t to say that some, or even many, people don’t use the phrase assuming that it is their constitutionally protected right to spread vitriol on the internet. But to imply that this is the only common meaning is disingenuous.