I think you're looking more for the "scheduling, managing pull from different clients" than the ability to backup to S3, Dropbox, local folder etc.

There are plenty of software projects to choose from for the latter. Borgbackup, Restic, Plain old NFSv3 and rsync, Tarsnap, Backblaze B2 etc.

I simply use a combination of Cron, rsync and Ansible to make backups to our central NAS, and that central NAS is mirrored to our off site NAS (with extensive snapshots and tape backups).

I had to use Netbackup for the Tape system which does everything you listed - managing and scheduling backup procedure in "clients" and does fine-grained schedule, show backup status etc. But, I HATE that thing with all my gut. It is one complicated pile of crap that I have to fight all the time to make it write to the damn tapes. Nothing like plain old simple Unix tools.