

I strongly recommend ZFS as a filesystem for this as it can handle your sync, backup, and quota needs very well. It also has data integrity guarantees that should frankly be table stakes in this application. Truenas is an easy way to accomplish this, and it can run docker containers and VMs if you like.
Tailscale is a great way to connect them all, and connect to your nas when you aren’t home. You can share devices between tailnets, so you don’t all have to be on the same Tailscale account.
I’ll caution against nextcloud, it has a zillion features but in my experience it isn’t actually that good at syncing files. It’s complicated to set up, complicated to maintain, and there are frequent bugs. Consider just using SMB file sharing (built into truenas), or an application that only syncs files without trying to be an entire office suite as well.
For your drive layouts, I’d go with big drives in a mirror. This keeps your power and physical space requirements low. If you want, ZFS can also transparently put metadata and small files on SSDs for better latency and less drive thrashing. (These should also be mirrored.) Do not add an L2ARC drive, it is rarely helpful.
The boxes are kinda up to you. Avoid USB enclosures if at all possible. Truenas can be installed on most prebuilt NAS boxes other than synology, presuming it meets the requirements. You can also build your own. Hot swap is nice, and a must-have if you need normies to work on it. Label the drive serial number on the outside so you can tell them apart. Don’t go for less than 4 bays, and more is better even if you don’t need them yet. You want as much RAM as feasibly possible; ZFS uses it for caching, and it gives you room to run containers and VMs.
Yeah, syncthing can do all of that except public share links. Run an instance on your NAS so there is always a sync target online.