Any experience backing up a MacBook to a remote NAS?

Using Tailscale I can remotely manage the home network so if I need to reach the Houston UI or TrueNAS GUI I can do so on my smartphone remotely. Using a mobile app terminal I can also SSH into all the devices on my home network. Both web GUI's are rather simple compared to what you would have to do on the command line to manage the same capabilities. If you go with Ubuntu LXD they now have a GUI for LXD and that works as well under Tailscale. You could install NextCloud and the wife may be able to handle that on her own without any difficulty.

Granted, the 45homelab hardware HL4, HL8, HL15 is not exactly inexpensive but it is more powerful as it's a full Mini-ITX AMD PC motherboard on the HL4 / HL8 and a Xeon motherboard for the HL15. You are paying for the more powerful desktop CPU and ports, etc. Over and above the low cost embedded CPUs used by QNAP / Synology, etc. Plus you'll receive outstanding tech support from 45 Drives.

The Houston, TrueNAS, LXD GUI's all support Apple Time Capsule emulation. It's a point, click, enable feature. The NAS will broadcast that it is an Apple Time Capsule and all the Macs will backup over the network to the NAS Time Capsule. This works on Synology / QNAP NAS devices as well. Using this method is a no brainer.

An alternative would be Carbon Copy Cloner which has some advantages over Time Machine and is the closest product to Time Machine.

I currently do this with ZFS based NAS devices. ZFS can snapshot to disk and send/receive snapshots over SSH to other ZFS based systems. I chose ZFS because it's ROCK SOLID. There's a Perl script called Sanoid that handles snapshots and sync replication. I use Tailscale as my zero-trust mesh networked VPN.

Yes, it works very well. ZFS send performs a delta copy of snapshots. First run is slow but subsequent updates are quick and depending on how often they are applied they can be very fast as it's only sending the differences.

Time Machine creates a sparsebundle file which is actually a directory with sub-directories and ZFS can see the contents as band files, indexes, etc. These files are written to ZFS and are easily snapshot to ZFS.

I would not recommend ext4 file system on the NAS to hold your Time Machine sparse bundle. ZFS is the way to go. Apple almost chose ZFS versus creating APFS and it seems to have been an Oracle / Sun Microsystems licensing issue for Apple. ZFS is superior to APFS but only because it was designed for servers and data centers. Apple also decided to exit the server market. So APFS makes sense for Apple products.

Check out 45homelab.com (from 45 Drives) they have nice 4-bay / 8-bay / 15-bay designs. 45 Drives created these products for home labs as the retail products were lacking in horsepower. Such as Synology, etc. I came to the same conclusion and have been DIY building my own NAS solutions. The software 45 Drives uses is called Houston UI which runs on Rocky Linux (spinoff from RedHat). But you can install whatever you want on this hardware. You can even buy the case w/backplane and supply your own motherboard. You could elect to use TrueNAS Scale instead of Rocky Linux w/Houston UI. Or you can install Ubuntu Linux and setup LXD snap package and still use ZFS for the disk arrays. You could also use the Ceph file system which can scale across data centers. Check YouTube there are a bunch of reviews of the HL4, HL8, & HL15 NAS products.