HomePods with not verify to my iCloud account

I have been fighting this for a couple of weeks with all of my HomePods; "Your Apple ID or password used to sign in to iCloud is incorrect."

I was using my HomePods to turn my lights off and on, but since then, I have just gone back to regular light bulbs since this has not worked for some time. It keeps saying there is a problem with my iCloud account.

So far, I have tried the following;

1) Tried on two HomePod minis with latest the latest firmware.

2) Tried on two 1st generation HomePods with the latest firmware.

3) I Tried from an iPhone 13 Pro, iPhone 13 mini and iPad Pro (all of which are on my account with the latest updates).

4) Tried from an iPhone SE running iOS 15.7 (that had just been reset).

5) I Changed my Apple ID password.

6) Removed all of the devices that act as a hub on the network.

7) Re-added HomePods as a new device (even removed from my Apple ID account), but I still had the same issue.

Interestingly, if I purposely put in the wrong password, it will reject it right away. However, when I put the correct one in, it will attempt to sign in for about five minutes, then back to that same screen.

Does anyone have any suggestions? I think it is fair to say this is not a hardware problem since it is happening to four different HomePods.