Apple - Shady password required for Update Apple ID Settings

You should ignore this and click cancel. This screen is an undocumented part of Apple's security practices (i.e. they don't mention it in their own documentation anywhere) and it exposes you to the risk that Apple will store, or could compromise (possibly resulting from a warrant/writ) your password for your local device.

This is documented further here https://privacylog.blogspot.com/2019/05/security-flaws-with-apples-two-factor.html