I would like the end result to include remote and encrypted backups.
I’m considering maybe a Synology NAS with an APFS partition for Time Machine and a BTRFS partition for Linux backups.
The Linux laptops might backup to the NAS with Restic.
The Synology NAS might then backup to BackBlaze or another cloud using Synology’s Hyper Backup or also Restic.
Have I missed a better plan?
Borgbackup. It is an ugly command line program. But it gets the job done and ticks all the boxes. But if you accept a recommendation try to use one of the friendly frontend like emborg or borgmatic
And you don’t need different partitions so you can save space.