I may have a clue about what the problem is.
I have an old Synology NAS DS213j. Under 15.01 I needed to turn off the firewall in order to make a backup. Somehow when I upgraded to 15.1 things worked. I though the bug went away.
But it scared me enough that I decided I should get a NAS that's not a decade old and can run modern software. So I bought a Synology DS224+ and installed it. I tried to backup using timemachine to it. It fails in the way everyone's been reporting. Turning off the firewall doesn't help. BTW 15.1 vs 15.1.1 doesn't make any difference.
There are two large differences between the working old machine and the new one. The new one is much faster. And the new one is running the 7 Synology OS where the old one is running the 6. I've done my best to use the same settings but in the new OS.
My guess is the bug has something to do with a timing error, and that turning off the firewall perturbs the timing enough that it doesn't appear for some people.
I'll try to call Apple tomorrow when their first string help desk is available. But I don't expect to get any more success than everyone else has had.