Why am I being asked for local password in 'update apple ID settings'?
With new hardware and new OS - Apple can entangle the local device password and keychain to cryptographically log in to your iCloud account / AppleID account without needing your password once the setup and initial hand shake to sign in with that iCloud/AppleID is completed.
This confuses a lot of people since they are expecting to enter an iCloud password and not the local admin credentials. This change is across watchOS, TVOS, iPadOS, iOS and macOS.
This also can be prompted when you do a setup / transfer:

iPhone asks for Mac password (or Mac asks for iOS password)
Why do our iPhones keep asking for passwords of other users?
Shady password required for Update Apple ID Settings

I feel this is much more secure overall since it mitigates if you have a key logger and if you lose control of your local admin - this means someone can't use Keychain Access to reveal your iCloud password - it just reveals a secure token that works with one device and can't be abused to download your iCloud data from another device.