Of course they control speech, that's absolutely on the EU agenda. Hate speech is not legal in the EU
The framework: https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=LEGISSUM...
It's extremely vague. It's more an understanding that "hate speech is bad so bad you should all draw a line... somewhere".
https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=celex%3A...
I think this is going to inevitably create more and more tension between EU and American contexts, because hate speech is affirmatively legal in the U.S., most recently ruled under Snyder v Phelps.