On my laptop, it doesn't nag me, but it does nag my son sometimes when he logs in. My son is not admin, so I don't know why Windows bothers non-admins with this.
At least I hope non-admins can't upgrade, but knowing MS, maybe they can.
That happened to me as well. I get told in the windows update dialog thing to check if I am windows 11 compatible, which I pass but I still don't get Windows 11 offered.