I wish I found this thread a two weeks ago, but I have some good news. After struggling with this for days, I contacted Apple. After days of back-and-forth calls with them, my third Advisor confirmed that in macOS 15.0.1 they introduced a bug in the Firewall feature, that they are working on a fix (hopefully a soon-to-be released 15.0.2), and there is no setting that we can make to create a firewall pinhole (which I asked for).
In the meantime the recommended work-around is to set Time Machine backups to be manual (not hourly or daily), to turn off the Firewall when ready to do a TM backup, manually kick it off, and (when it is done) to turn the Firewall back on. Effectively, we have to "lower shields to use the Transporter" (Trek fans will recognize the analogy). It sucks, but at least it gets the job (sort of) done.
I would recommend, before you run your next TM backup, you "lower shields" (Firewall) and option-click on the TM Menu Bar icon to run a Verify process to be sure that this problem hasn't corrupted your TM backup. After this happened (on October 3), my TM back up was corrupted and I had to start over (twice or three times during the debugging process).
[Edited by Moderator]