When you create a folder in syncthing-android, you should see two entries in the folder picker list ending with /Android/data/com.nutomic.syncthingandroid/files. One points to a folder on the internal storage and the other one is a folder on the sd card. When you choose the sd card, you can create new folders there which are writable.
This solution, however, only works when the folder location doesn’t matter. You cannot use it to share data that was written to the sd card somewhere else by another app, like the DCIM folder.