Asked to verify an existing Apple e-mail address after a password change

Hi there, I'm hoping someone may have an answer to the following problem.

I have recently changed the password associated with my AppleID (e-mail address). I made this change on my Mac and did all of the necessary updates across the other devices that I own (MacBook Pro, iPad, AppleTV, etc.). This all worked fine and I'm able to use all of the devices without any problem. However, when attempting to sign into appleid.apple.com to generate app-specific passwords for some of the 3rd parties Apps that I use, I then ran into difficulties. Specifically, after signing in with my e-mail address and password, I am sent a 2FA code, that I then enter. Directly thereafter I am prompted with the following message "An unexpected error occurred..." and am then required to "verify my e-mail address" - this is the same address that I use as my AppleID. When I attempt to do this I get the following error message "This email address is not available. Choose a different address.". This makes no sense because I'm not using this address for the first time - it has been my AppleID e-mail address since 2005. And this is where the process ends i.e., I am unable to sign into appleid.apple.com (nor for that matter into iCloud via a browser because the same sequence of events happens when I try signing into iCloud too).

I'm using Safari on my Mac and IoS devices - the sequence of events described above is the same regardless of which device I use to try to sign-in to appleid.apple.com.

I'm running macOS Monterey v12.4 on my Mac devices and iOS 15.5 on my iPhone and iPad.