Putin chillingly calls for ‘self-purification’ of Russia from ‘scum & traitors’

Not really. It gets pointed out in the news a lot because it's so salacious, but it's not at all common really. 2016-2020 saw a bit of an uptick in that kind of name-calling though, as the Trump administration implemented various policies and emboldened those with a pre-existing preference for authoritarian societies/systems, in spite of their self-professed "love of freedom".

Source: self; former-Republican. Never again. America no longer has a conservative political party. What we have now is a nationalist authoritarian movement that borders on delusional, leveraging emotional contagion theory and group identity/identity politics to manipulate otherwise well-meaning (if gullible) people into supporting would-be tyrants.

No, people in the US call folks who embrace fascist policies and ideals Nazis. Because, you know, Nazis and fascism go hand-in-hand.

Not all Republicans are fascists, but there's far more overlap there than in any other major US political party.