To answer your question: LLMs don't have free speech, because they aren't companies/businesses, they are a tool (that is used by companies/businesses).

Whether a company/business uses an LLM or a real human to write a particular piece of text, that piece of text is entitled to free speech protections on the basis of the company signing off on it. Not on the basis of how that piece of writing was produced.

I appreciate the answer and the open minded thoughtful answer.