How do I update iCloud with new password on Mac if it is stuck?

I brought this MacBook Pro 2012 back to life after 10 years of inactivity, and I reset the iCloud password successfully, but the Mac is still holding onto old passwords I can't remember, how do I update iCloud with the new password on Mac if it is stuck like that? I deleted the keychains associated with iCloud, but that didn't seem to release the old information. And the email on the mac is correct, I receive the permissions on my phone for the mac to log in.

The other factors are that I have 2 factor authentication enabled on my phone. I logged fully out of iCloud on the mac, and logged in fresh into the iCloud app on the mac successfully. But, the iCloud prompt is still popping up, asking for a password that seems to not match the newly made, correct one.

I also can't access the Keychain section on iCloud permissions on System preferences with the same iCloud credentials.

I'm wondering:

What location in the mac would be holding onto this information so I can refresh it with the new password for iCloud or delete the containing file for reestablishment?

Thanks!