For what it’s worth, Time Machine doesn’t seem to care as much which file system it goes to anymore, as long as it goes over SMB.
There are specific config settings to make it work , but nearly all servers , including synology, will have a button that does whatever the magic combo is.
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.
For Macs: I use Time Machine backups on unraid (nothing fancy but it has built in settings to support it effortlessly). There’s also https://hub.docker.com/r/mbentley/timemachine that I tried out a year ago.
I haven’t tried over vpn but as long as you can mount the share , it should be fine.
Both Synology and qnap makes solid products. Just make sure whatever file system you pick for the NAS that it can do snapshots. Wasabi is better if you are long term archiving, but for backups that churn, BB is way cheaper. LGTM.