I found this link. It says that even though TM deletes old backups, you might run out of space on the drive.

https://support.apple.com/guide/mac-help/if-the-time-machine-backup-disk-is-full-mh15137/mac

I too thought I would never run out, but be asked that I might have to delete some information from older backups.

Are you sure the message is just not telling you that it has run out of space and thus will be deleting older information? I have gotten the message I just described, and it scares you/me.

If indeed for some reason you can’t get TM to work on this drive: You could re-format the drive and start all over with a new, first time, backup (which will take quite some time). Another suggestion is to get a new drive and make a new backup. Eventually the first drive will die, at least this way you start its replacement before the old one dies.

I am a newbie. Same was happening to me on Firefox. Then I switched to Safari and that seems to remember my log in and lets me in. I am wondering if it is a browser issue (I have ad block on Firefox running).