What you call 'extreme left' would be considered 'center right' in Europe.
For instance, the US has legal gay marriage when it's still banned in some European countries and legal marijuana when it's only decriminalised in most of Europe. DEI is also bigger in the US, and so are ideas like defunding the police, reparations (for slavery or colonisation), etc which don't get as much traction in Europe.
On the other hand a lot of the traditional left-wing ideas like heavy state intervention, actual socialism, workers' rights are bigger in Europe and several countries have actual communist parties with parliamentary representation.
But then again, most European countries are states for a specific ethnic group which would absolutely not fly in America, Canada, Australia etc. For instance, German right of return lets anyone of ethnic German descent from Eastern Europe claim German citizenship.
Let me remind you that EU actually does deport people all the time in practice - US is considered very "illegal friendly" by our standards, as it's practically impossible to live like that here due to all the necessary bureaucracy and approvals to have basics such as healthcare, employment, bank account and payment card (necessary as cash payments are limited to small amounts - you can't even buy a car with cash legally), a place to live... While a not uncommon practice in the US. Nobody here understands that you can actually get "legalized" after/during an illegal stay in the US - it's impossible around here, being illegal puts a permanent black mark on your passport.
There is an entire police department just for dealing with foreigners and catching and deporting illegal residents. All foreigners must register with that department, renew their registration regularly by personal visit on the police station, show up at the station when they are randomly summoned, allow the police inside their residence for a random check - and the police will actually check things like - is your wife actually your wife or is it a trick, are you actually working where you said you work, are you housing more people than you should and what's their status, etc. All foreigners must keep their address of residence and contact information updated, and just having that wrong can be enough to get deported - and it will happen, sooner or later, even if they find out years later and you have corrected the mistake in the meantime.
All this is nothing new, it's always been this way. It's one of the major reasons why the US is taken as land of freedom - the ability to just come in and work there, with personal rights much closer to what the citizens get, is a freedom that we ourselves don't offer, EU states require you and your employer to prove they tried and couldn't find someone local first; and good luck without an employer sponsoring you - you can't get health insurance and bank account without an employer in my country (with an exception for students).
And half the EU has a very bad opinion about anything resembling socialism.