Safari prompting for local user account password on Apple websites
This is a new feature with safari on macOS and Catalina when you are signed in to your iCloud / AppleID on trusted and keychain synchronized devices when communicating to some Apple secure services online. 

Your local admin password unlocks they key store and sends a secure token rather than your iCloud password to authenticate you through Safari to Apple’s web site. 

Ways to opt out:


Sign out of iCloud on that Mac. 
Use a different browser.