hakayova long-time Syncthing user here. I didn't have to do anything unique under GrapheneOS to get all of my shares working.
Ensure you have granted Syncthing the necessary storage permissions; either allow all, or use storage scopes to specify a folder that will hold your shares, such as a root folder called Sync (the full path will actually be /storage/emulated/0/Sync in the Android system).
When adding a share from another remote host, Syncthing should prompt you to specify where you want to store the new share on your phone. You would enter a path such as, /storage/emulated/0/Sync/Music for your music share. You shouldn't need to change any of the other share settings unless you have a reason to. If I recall correctly, Syncthing will automatically create any sub-folders as needed without further intervention; just ensure the Folder Path is correct before saving the new share.