If it’s happening every 15 minutes, it’s probably a systemd timer trying to kick off a unit on a schedule. Check for .timer files in your system and user systemd configuration and see if there are any configured to run every 15 minutes.
Whatever process is trying to start is probably exceeding the open files ulimit. ulimits can be set system-wide, per user, and per cgroup.
The ulimit may be too low, there may be some process leaking file handles (opening files periodically but never closing them), or the unit might be configured to run under the wrong user or cgroup.
If a reboot gets rid of the problem temporarily, it’s most likely a file handle leak. Remember that objects like network sockets also count as files for the purposes of the open files ulimit.
A tool like lsof can help you track down processes with a lot of open file handles.
For me, I only back up data I can’t replace, which is a small subset of the capacity of my NAS. Personal data like photos, password manager databases, personal documents, etc. get locally encrypted, then synced to a cloud storage provider. I have my encryption keys stored in a location that’s automatically synced to various personal devices and one off-site location maintained by a trusted party. I have the backups and encryption key sync configured to keep n old versions of the files (where the value of n depends on how critical the file is).
Incremental synchronization really keeps the bandwidth and storage costs down and the amount of data I am backing up makes file level backup a very reasonable option.
If I wanted to back up everything, I would set up a second system off-site and run backups over a secure tunnel.