>I got the impression that free speech in the US is limited to right to annoy people and harass politicians from distance.
That's a pretty trite way of looking at it. You could see for example how important free speech was to the US' civil rights movement in making sure that people were able to organize to challenge the status quo.
>.. if it was in US they could have been removed and have their free speech in a designated area simply because they don't want them there.
US' citizens generally have a better time in courts challenging such things than Europeans do, however.
>In contrast, in most of Europe you usually can approach and ask politicians whatever you like.
But can you tell them whatever you like without facing repercussion if they don't like what they're hearing? No.
In the US, you can still exercise your right to free speech to inform your fellow citizens about the genocide of Gaza - in Europe, most definitely not so easy. (Some European states, its easier than others ...)
US civil rights movement? Seriously? Different times different people. In the latest free speech crusade a rich guy just changed the kind of speech is allowed on his platform. Online speech is heavily restricted on US platforms, as accounts are shadow banned/rate limited/deleted all the time. What freedom of speech examples do you have that involve living people? Every single one freedom of speech fighter are fascist who demand some other speech be suppressed and theirs amplified. Remember their attitudes over the Charlie Kirk assassination reactions?
I don't really care about the courts in this, you win in court and never speak again anything new because you don't want to go through all this again.
And who cares if you can tell someone something if you can't engage with them. Are you casting a spell? why would you care someone hears you? In USA they take you to safe distance behind some barriers to tell your thing. Useless stuff.
I don't know why you believe that you can't inform people about the genocide of Gaza in Europe, in fact Europeans are significantly more informed on this and having flotillas and what not.
US free speech seems to be performative. Its even limited to words, they try not to say the N word and do all their racism without that, then they are relieved when they end up saying the N word and claim freedom of speech win. It's weird from European perspective.