what would cause appleid.apple.com to ask for my mac password to login

Because you need to login.

See the following Apple articles:

Reset your Mac login password

https://support.apple.com/en-mn/guide/mac-help/mh35902/mac

Change the login password on Mac

https://support.apple.com/en-gb/guide/mac-help/mchlp1550/mac

Ways to remember passwords on Mac

Ways to remember passwords on Mac – Apple Support (UK)

Sign in with your Apple ID

Sign in with your Apple ID - Apple Support                               

Sign in to your Apple ID preferences on Mac

Sign in to your Apple ID preferences on Mac – Apple Support (UK)

Set up your Apple ID preferences on Mac

Set up your Apple ID preferences on Mac – Apple Support (UK)

that recent password change is correct.

Then see -> What to do after you change your Apple ID or password

What to do after you change your Apple ID or password - Apple Support

FYI: You are sign in here .  .  .  with your Apple ID & Password (?).

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.

Click cancel in the window asking for your Mac password, then you can login with your Apple ID password