My iCloud password doesn’t match my Apple ID password
I received an email from Apple that my iCloud account was locked for security reasons and I needed to reset my password. I did that, but now my regular Apple account has the new password, but the App Store/iTunes and devices still only respond to the old password. Asking "How to reset App Store password" and I get instructions to change the Apple ID password. I could change the Apple ID back to the original, and everything will match again, but that seems to be defeating the purpose - whatever it was - for Apple locking my account. Suggestions?
[Re-Titled by Moderator]
MacBook Pro 16″, macOS 14.4