Which "freedom of speech" does? European Freedom of speech has quite a few caveats too.

There were cases where people lost their jobs for their extracurricular legal activities that were hate speech according to someone. Like in US, private companies seem to give in much quicker than government that tries to follow the law to the letter.

The general notion of what it means for speech to be free, not a legal protection of that notion.

Usually because that's the only place it's really codified into law or any other legitimate document in the US. The Supreme Court has limited the scope of the first amendment, but that's all just implicitly codified via past decisions and opinions - a less discoverable format I've yet to find.