Earlier quoted context omitted.
If you think internet surveillance is an EU first, you will be delighted to read about PRISM
I think nobody in the EU believes that America is the country of freedom and privacy and anonymity. (Boolean and) I guess what the OP meant is that in EU you might have the police knocking at your door for some reasons you don't have in the USA, not because they don't have data about you, but because in the USA you have some very strong constitutional rights that are really hard to bypass. Twitter, Tiktok, etc could…
You might get a few more of them. Recently a bunch of French people received jail time for repeatedly posting how the president was a pedophile and his wife was a man. Because, you know, harassment is illegal in many European countries. But the only obligation by the service provider, if asked, would be to delete the posts and give the user's IP address.
The EU Digital Services Act is actually a much wider liability shield than the USA's Section 230. I suggest reading it. ISPs ("mere conduits") have basically absolutely immunity, and caches merely have to ensure they make an effort to delete the cached object when the original object disappears (i.e. they have a reasonable expiry time) to be immune. Social media, since it's a content publisher, has more obligations, of course, but they are also not that onerous and things like automated scanning are only required if your site is big enough to afford them.