How to resolve multiple Time Machine issues on Ventura 13.7.8?

Multiple Time Machine problems:

I’m on Ventura 13.7.8 on an older iMac. I reformatted a 4TB WD hard drive that originally was a Time Machine backup. Finder says all 4TB are available but I can’t set it up as a new Time Machine backup because it shows  these messages (below). All together, the “backup” blank disc is on the desktop but TM can’t find the disc and I can’t make the HD backup because Time Machine thinks it was interrupted and can’t do anything until the non-existent backup finishes. Any suggestions?

[Re-Titled by Moderator]

Original Title: Time Machine backup