It just started happening to me today. Hasn't ever happened before. I may have fiddled with some security settings yesterday but I didn't write down what I did.
The problem appeared after I had my machine running over night but with Lock Screen set. I logged in normally, the Studio display came on as usual then I got the dreaded message. I've Shut Down completely but didn't turn off power to any parts of the system, then Restarted. But to no avail. Then it happened again pretty quickly.
I've watched this thread occasionally since
@Jamacfer 👏 first posted. TimeMachine is an important part of my setup. Thanks to all of you for commenting, I'll look through the thread and see what's been said so far.
I'm running Sequoia 15.3 on Mac Studio M1 Max 32GB 2TB, with two WD 10TB hard drives (one is has 4.6 TB used, the other has 6.92 TB used) attached to a USB extender, which is attached to a single USB port on the Studio. They're used as A and B TimeMachine disks backing up alternatively every hour.
The extender has 5 ports, two are used by the TM disks and they each have their own power adapters. Interestingly I'd plugged in external portable speaker into a 3rd in order to charge it. It's drawing power from the extender and therefore the Studio USB port.)