Password works some places, not others

This is so aggravating! I'm hoping someone can help me.

I'm on a 2014 Mac Air, up to date with Big Sur.

My Apple ID and password are working just fine on the App Store and in Preferences, to change my iCloud stuff.

But when I go to appleid.apple.com, it won't accept the same password. It just won't. I've moved right from the App Store to the appleid front page - with the same password copied to paste. It works in one place and not the other.

Any idea what the problem might be? I do need access to the website.