This is fairly anecdotal.

I wish when people use the term woke they would say what they actually mean. I suspect they don't because they don't want to be seen as racist, sexist, homophobic, or whatever. What do you mean by woke?

The "left" is huge and diverse (which people don't know because left-wing thinkers don't get the adoration and amplification right-wing thinkers do in this country.)

I am guessing you are referring to Marxist-Lennonists, or even Tankies. Folks who believe that only class oppression is worth fighting, and that the solution is centralized authoritarian regimes with left wing people in power. Those folks are generally anti-liberal, despite being on the left, and deny any history that would complicate their politics.

Alternatively, you might know neoliberals, who believe in the power of capitalism to address social problems and deny any history that might complicate their politics.

Or you might know Syndicalists, who believe unions are the path to worker's political power, and who deny any history that might complicate their politics.

Etc.

If you know one "very left" person, you know one very left person.

“Wokeness” is an elusive term that is the best attempt to describe a wildly variable but seemingly consistent pattern of beliefs and actions. My left-side friends disavow “wokeness” but still agree with many of the problems “woke folk” identify.

As an outsider, it seems like the moniker of woke best applies to the pattern of thinking that broad problems have a simple and heavy handed solutions. Furthermore, criticizing such solutions will put you in the same camp as those committing the offense, even though you may agree about the problem.