After a Windows11 update re-boot, I had to sign-in on many things - Firefox was one of them. When I tried, I entered my name and password with no errors. But, then I was asked to verify that I was me by signing on to my YouTube app on my tablet.
I have no intention of keeping this "malware" but did download it to get access to Firefox.
Please change the secondary verification for something else.
Unless you have sync that would be why your being asked for the password. Youtube has nothing to do with firefox browser other then opening in firefox.