No, we think woke is hysterical because no right wingers know what it means. I'll happily call myself woke, but I also use it as a sarcastic pejorative
I think Americans need to absorb a bit more global context about the left-right spectrum. I see people saying that policies like universal health care, access to abortion, basic worker rights and affordable education are "far left". Most of the proposed policies of the left in the US are centrist in the rest of the Western world. Unless you are advocating for a Communist regime along the lines of the Soviet Union or Maoist China, you aren't really "far left". Similarly, unless someone is advocating for a fascist dictator state, we should probably not call them "far right". Of course, that is what Trumpists advocate for, so they really are far right!
Council communists and Anarchists generally qualify for far-left status. (Or, differently put, council communism is methadone therapy for Marxists who don't yet dare make the jump to syndicalism).
authoritarianism and far-left are mutually exclusive.
You're correct, believing that "authoritarian" is a well defined or meaningful term and not just a snarl word created during the cold war to equivocate communists and Nazis is incompatible with being far-left
