Trouble with TimeMachine using macOS GoldenGate
I'm actually posting this for anyone else who has the same problem with Time Machine that I did, so that they can learn what fixed it.
I have a brand-new Mac Studio 64 GB with a 4 TB internal drive, which I just got this week, which means my first OS on it was macOS Golden Gate 27.0. I was setting up my backup TimeMachine disk, which is an external HD, Western Digital D10 8TB drive. I formatted it using APFS, GUID with Disk Utility. I then used the TimeMachine menu under System Settings to Set Up the drive for use as a TimeMachine drive. Everything looked good until I tried my first backup. After clicking Start Backup on the TimeMachine settings menu, I got the usual "preparing for the backup" message for a few seconds. Then instantly, everything stopped. I got a notification message on my screen saying "BACKUP NOT COMPLETED Time Machine couldn't back up to "Backup1"".
I spent many hours over the next two days trying to search for answers. Reformatting drive repeatedly, trying First Aid from the Disk Utility, countless manipulations in the Terminal window based on search/reddit/AI suggestions. Nothing worked.
Finally, after using the Console app to record the log with one of the failed backups, and reviewing the log with the help of AI, it looked like iCloud's FileProvider was interrupting the Time Machine because it was hung up on trying to sync iCloud. I tried multiple permutations of turning iCloud on/off, signing out/in of iCloud. Finally, what helped my was removing the other two users from my Mac using the Users and Groups under System Settings. Apparently it was the iCloud on one of those accounts (my wife and son who virtually never use my computer); the User accounts were a holdover from a prior computer years ago, and were carried along with the data transfer from my old computer when Migration Assistant helped set up my new computer.
Moral of the story: look in other User Accounts for processes that were interfering with the backup.