Why did my Time Machine stop backing up on iMac running macOS Ventura 13.7.6?

iMac running macOS Ventura 13.7.6 ceased backing up 5/10/2025. Many hourly backups were automatically completed prior to failure:

Message: Time Machine couldn’t complete the backup to “Mac HD.” There were no disks found to back up. This can happen if all available disks have been excluded from the backup. Click Options to edit the excluded items.

Explanation: The LaCie device holds the backups. The cable is properly seated directly in the iMac port. The Mac HD is the internal hard drive being backed up.

For no known reason, the Mac HD is listed under "Exclude from Backups" and cannot be removed. That is, clicking the grayed-out minus sign in an attempt to remove the drive has no effect. First clicking the Mac HD entry causes the grayed-out minus sign to cease being grayed-out. But, still it cannot be successfully clicked.

Note: I found two prior reports of this problem in a single thread within the Community but the thread has aged out and cannot now be modified.

[Re-Titled by Moderator]

Original Title: Time Machine Stopped Working