Opps I signed in with a different ID Disregard SeekerPA another ID of mine
Its always possible for corruption in the OS, or hardware issue. Time Machine is pretty simple and mistake proof. Years ago I had a hard drive I was using to backup with Carbon Copy Cloner and had a terrible time completing the backup and it turned out to be marginal and was relatively new and replacing resulted in a smooth backup experience. That's why trying another HD might be revealing. This difficulty I suppose you have shut down and restarted and still have the problem. And your OS is 12.5.1 the latest. My computer is a MacStudio with the M1 max chip and I use a USB drive for TM with no issues. I have never had a HD fail, but had two new ones that never worked right at the start and spent time thinking it was something else wrong and had the opportunity to return one to the store rather than work with a doubtful customer service rep and got something else that proved to be trouble free. If your HD is new, calling the manufacturer for help might bring a replacement as some advertise their HD is "perfect" for TM. This is my limit of understanding.