Governments often try that kind of nonsense. Usually against organized crime, terrorism, child abuse.
But in the end it’s just used for the heavy crimes like copyright infringement
Still they try because there is always an exception that allows breaking those laws.
Chat control isn’t something the EU invented, they tried to implement CSAM in Apple devices and the whole chat control thing in the EU was heavily lobbied by Thorn https://en.wikipedia.org/wiki/Thorn_(organization)
I don't think they do. They have constitutions that guarantee "Freedom of Speech" or "Expression," but don't define those terms in any way. I don't know that any of them lack legally prohibited political speech laws.
I feel the US was the origin of this "Hate Speech" nightmare that has been growing to encompass all of Western politics over the past 30 years, but the irony is that you can do slurs all day long in the US, to anybody you want, whenever you want. You will probably be ejected from the premises, though. In the US, the speech still has to be connected to a crime. In the EU, the speech itself is the crime.