Well, when I say "connotation," I'm referring to the manner in which it's intended to be wielded.

Obviously, the original incarnation of "woke" amongst Black people was to stay alert and aware when it came to injustices and the solutions for them. It sounds as though that original intent is what much of your social circle still wants the term to mean.

The connotation of "woke" has been changed, over time, once the term got hijacked by different factions.

White liberals often manipulated "woke" as a way to pressure other White people into deferring to (or conforming to) dialogue raised by much of the academic intelligentsia when it came to race relations.

White conservatives rebranded "woke" as a way to demonize anyone who desired structural reforms challenging the status quo, such as increasing multiculturalism and equity. Now, the MAGA-adjacent wings of the Republican Party are supercharging that deceit.

I also agree with you that it was never the primary objective of all White liberals to propagate this brand of shame and guilt just for the hell of it. However, I do believe that invoking shame and guilt has been viewed by many of them as a tool through which they could shut down dissent or debate. That ties into what you've already pointed out -- how they may not always be doing it effectively or correctly.

And, it by no means excuses the mangling of "woke" amongst White conservatives...I'm just pointing out that it's a backlash by many on the Right to such behavior from many on the Left. It wouldn't be my specific response (I prefer nuanced discussions), but I can certainly recognize where it came from even when I oppose the Right's tactics.