Unlike you, I believe that women are real and have agency and they are not the creation of the Patriarchy. Not all of those women are perfect. Some of those imperfections are shared.
If all our language is the creation of the patriarchy, as you imply, I can only use patriachial language to describe anything, including women.
But what of a gay man. The Patriarchy subjected him to awful prejudice and horrific and dehumanising punishment. Are gay men part of the Patriarchy.
Men, including white men, have been enslaved throughout history. Are they the Patriarchy?
What of weak, stupid, inadequate men? The Patriarchy exploited them. Sending them down mines, out to sea and off to war? Are those inadequate men the Patriarchy?
Before the first women were given the vote in 1918 half of British men didn't have the vote. Were those disenfranchised 50% the Patriarchy?
But to return to Karen. I confess I didn't know that the term was coined in Britain. But we do share our language with Americans. We can't just ignore what words mean to them. The term Karen is now being used to describe men, which arguably empowers women and removes the misogyny.
The one thing I wrote/implied that you don't seem to disagree with is that women complain/ make a fuss more than men. That really is the heart of the issue.
Sorry to have derailed your thread OP, but I share responsibility with the people who complained/ made a fuss about your language. If only we had a non-sexist word to describe them.