FreeFileSync detects moves and changes quickly without rereading the whole file. The first time you sync it will read every file to hash them first, this takes a long time but subsequent syncs will be fast.

Change the full-rescan interval to monthly, or yearly even, problem solved.

Why do you need the files in your local?
Is your network that slow?

I've heard of multiple content creators which have their video files in their NAS to share between their editors, and they work directly from the NAS.
Could you do the same? You'll be working with music, so the network traffic will be lower than with video.

If you do this you just need a way to mount the external directory, either with rclone or with sshfs.

The disks on my NAS go to sleep after 10 minutes idle time and if possible I would prefer not waking them up all the time

I think this is a good strategy to not put additional stress in your drives (as a non-expert of NAS), but I've read the actual wear and tear of the drives is mostly during this process of spinning up and down. That's why NAS drives should be kept spinning all the time.
And drives specifically built for NAS setups are designed with this in mind.

Syncthing should have inotify support which allows it to watch for changes rather than polling. Does that help?

Nothing wrong with rsync, it's still kinda the shit. Short script, will do everything

https://git-annex.branchable.com/ this thing extends git to handling lots of big files. Probably a solid choice, haven't tried, but it claims to do exactly what you need, and even has ui and partial sync

You are correct that a reboot will trigger a full rescan. I'm always on the lookout for better sync. I just don't think it's out there right now for easy bidirectional sync.

Basically, if you want to set and forget, Syncthing is the best option. If you want more control, you'll need to look into setting up rsync scripts or similar, which will at least better let you control how often to sync.

You could try FreeFileSync. I use it for pretty much your exact use case, though my music library is much smaller and changes less often, so I haven't tinkered with its automation. Manual sync works like a dream.

Ad others have said, nextcloud won't rescan or reindex on a reboot. no idea why sync thing does, and surely there must be some way to disable that, too. I'm still hesitant to recommend NC as it's somewhat fragile, needs way more babying than I'm willing to keep up with and just does too many things, none of them anywhere close to "well". File sync on real computers works solidly if you have a reliable connection (don't get me started on Android).

Have you considered using a real media-hoster, like Jellyfin (or like a dozen others)? Jellyfin works fine for music (the are other music-only solutions though). There are plenty of clients that can stream, and have offline support (download a subset/albums/playlists) for things like laptops, phones, ... The server can usually transcode audio formats that a client can't play, in real-time, if needed.

Edit: I realize I wasn't clear as to what this means in practice. You essentially get a self-hosted Spotify. Your library, run from your server, optionally you can connect to it from anywhere.

I have a very similar setup to yours, a relatively large music library around 1.7TB of mostly flac files on my server. I'm able to organize these files locally from my laptop, which at various times has run either OSX, various GNU/Linuxes, or Windows. However I do not bother pushing the files themselves back and forth over the network.

Even if I did, I wouldn't automate the syncing, I'd only run it manually after I'd done my organizing with Picard for that day. After all, it the organization with Picard isn't automated, why should the syncing be? I'd probably use rsync for this.

In actual practice I do this: Connect to my server from my laptop using ssh, forwarding X. Run Picard on the actual server through this remote connection. Picard runs just fine over ssh. Opening a browser from a Picard tag for occasional Musicbrainz.org stuff is a little slower but works. I would then use a tmux or screen session to run the rsync command when I'm done with Picard for the day for syncing to a backup if necessary.

I don't really bother keeping a whole copy of my music collection locally on my laptop or phone though, since It's been bigger than is practical for a long time. Managing multiple libraries and keeping the two in sync turned into such a hassle that I was spending more time organizing than actually listening (or making mixtapes/playlists). To listen to my music locally I've used either Plex or Jellyfin, sometimes MPD (like when my server was directly connected to my stereo receiver), or just shared the folder via samba and NFS.

I use Nextcloud to sync a huge music collection and it works great - I was kinda surprised

I run it on an underpowered NUC and it behaves beautifully

I used seafile in the past. but I abandoned it for syncing. might help your use case ...

I suspect it's somewhat inevitable, since in order to sync you need to know what's the difference between files here and there (unless using smth like zfs send which should be able to send only the changes, I guess?). I'd probably tag everything at once and then sync

Have you had a look at "Lucky Backup"?