Time Machine backups fail after a month or so

I’ve dedicated about 4 TB to back up about 1.6 TB. When I create a new share of that size, and designate it for Time Machine backups, it works fine for a while. Inevitably, the backups start to fail after a few weeks saying either insufficient disk space. Time Machine is supposed to delete old backups and replace them, and it used to.

If I delete the backups from Time Machine, it doesn’t help. The only solution is to delete the share and recreate it. I’m on my 5th iteration, now. Tempted to go back to using a USB connected disk, but want to ask here first.

The Catalina 10.8 help for Time Machine https://support.apple.com/guide/mac-help/if-the-time-machine-backup-disk-is-full-mh15137/mac is contradictory - on one had it says “…Time Machine deletes older backups to make room for new ones.” but the next sentence says “You may be able to use Time Machine for a long time before running out of space.” Not sure there is any server-side solution for this.