Scientifically race does exist in the sense that humans with certain genotypes can present certain phenotypes but we are all the same species. I don’t think you can really quantify it at the individual human level though without ending up with all this old fashioned racist concepts coming into play, i.e. someone with 1/8 asian hertiage is “still asian” or whatever.

Race seems to be a bigger deal in the states because it is more politicised in terms of voting blocs. That’s not to say we are immune to it in Europe like people with south asian heritage often vote for particular candidates in the UK for example.

I think one major factor in perceived differences is that our larger cities in Europe tend to be more genuine melting pots with fewer segregated areas. There are probably other reasons like having a stronger sense of civil society too.

tl;dr: race is real in a fuzzy sense but not particularly important. Europe has a different culture to the USA in some key senses.