Möbius Sync doesn't sync in the background; you must have the app in the foreground for it to function. So, not quite a proper substitute for Syncthing, but may work for OPs usecase.

Of course it syncs in the background. It‘s just not instantaneous, because iOS severely limits what you can do in the background.

Right, it does the best it can given the limitations of iOS, but "not instantaneous" can mean hours before synchronisation happens. When the phone's charging, or when the app is open, then it does tend to work almost as well as on Android.

Weird -- at least when I tried it, I couldn't get it to work in the background. Maybe it was working, but not reliably?

Nope, it does sync in the background, just few minutes ago I had a notification that it synced.