Interestingly, while I get what you're saying - and can agree that "screeching" probably is at least slightly gendered when applied to humans - in my experience

Interestingly, while I get what you're saying - and can agree that "screeching" probably is at least slightly gendered when applied to humans - in my experience I've more often encountered "screeching" applied to non-human entities, like birds. Enough so that I would not automatically make any connection to the use of the word "screeching" as specifically being a gendered derogative aimed at women (although context would dictate a lot about the interpretation of any specific case of course).