Wake on LAN won't work remotely, so you'd either need to have access to a VPN at their location, or have a 2nd always on device that you can connect to and that could then WoL to your device... or... get a device with an IPMI which you remote into. (All non-VPN forms of remote connection are open to abuse)

I suspect (guess) you're not going to be able to setup a VPN, so perhaps an always on pi is going to be necessary - so maybe it'll be that with drives set to spin down when idle?

OpenMediaVault was my preferred choice until everything went docker on it which was getting too complex for a NAS... so I just created my own, which powers on at certain times of the day and off again when CPU / network IO was low enough.

Data transfer with syncthing is great, but I don't really recommend sync for snapshot backups... (consider your files are all corrupted, it'll happily sync those corruptions) but I have enough space for a few versions of my files, so in theory I can roll back, but it's cetainly not a Grandfather, Father, Son strategy.

What are you using for your main backup? It probably has a feature for doing remote backup / duplication. You're best off using that.

If you don't, then I think that's probably your first order of business. There are a bunch of good COTS NAS devices that support remote backup to a similar device or to the cloud. Synology generally seems to be the easiest to use based on reviews, but recently they've been getting picky about hard drive support.

If you'd rather DIY then there are some FOSS software options to let you build your own NAS and then back it up to the cloud or to a remote device running the same software. These can get pretty complicated from what I can tell (I'm in the process of doing something similar, been researching). Options include OpenMediaVault, and TrueNAS. TrueNAS seems to be "better" but more complicated and easy to fuck up.

Unraid is also very popular, but it costs money to get a software license. Users swear by it, though.
And on the outside HexOS - a fork (or maybe alternative front end?) of TrueNAS, by some former Unraid devs, with the goal of making TrueNAS as easy to use as Unraid. But it's both paid and beta, so probably not a good choice yet.

These will all allow remote backup to cloud or to a remote device running the same software. They also typically support some kind of virtualization with an app store, so you can use your NAS to host other servers like a media server or immich or home assistant, etc (although app ecosystem abundance will vary).

Wrt hardware, you'll have to look up system requirements for the software you want to use. For example, TrueNAS uses ZFS filesystem, which wants a lot of ram if you need it to perform well.
If your r-pi can run the software you want, then you can get a SATA hat for your pi, to run a couple hard drives. You can also get NAS cases for your pi.
I probably wouldn't recommend leaving a mess of cables and parts at your friend's house across the country, it's better for both of you if the system is fairly well contained - enough for them to move it without risk of parts getting disconnected.

raspberry pi + USB raid enclosure in mirror mode with 2x HDD

Depends a little of how you set it up. But for the target system at least use some kind of raid/raidz. With ZFS you can do "zfs-send" perhaps? Or something like good old rsync would work to.

I have a remote backup setup at my parents, which consists of a rpi4 and an external hdd (old NAS HDD). The rpi also has a wireguard interface running. If I need to back stuff up (via a restic-rest container) I open the vpn from my side, start the container, mount/decrypt the hdd and trigger the restic update. Afterwards everything gets disconnected again.

The rpi needs to be always on and you need to be able to forward a port to the rpi.

The data should be secure though, as the disk is encrypted and not mounted. (You can even store the decryption key on your side of the network, so you need the vpn to be able to mount the hdd)

I would consider also the case where something goes wrong. Maybe the whole thing crashes, maybe you misconfigure something, maybe there's a power outage or something else happens and you lose the connectivity. Is there someone on site who can do anything to your hardware as you can't easily just go and figure it out by yourself?

If the answer is 'no' then I would strongy reconsider the whole approach. On a worst case scenario the system goes down before you're even back home from the trip and then your hardware is just gathering dust.