syncthing is a great choice, I've been happily using it for 2 or 3 years across Linux, Android, and Windows. I've never had to do anything special to use an SD card on Android.
It appears newer versions of Android do not provide a way for apps to access _external_ storage using ordinary POSIX APIs. SD cards can be used to back and provide "internal storage" on Android, and I don't think that is a problem (yet).