I was able to fix this by doing the following:
- I used AppCleaner (AppCleaner) to fully remove Syncthing
- I deleted the Syncthing.dmg file and permanently removed it from Trash (this step was probably optional)
- I re-downloaded Syncthing
- I opened the Syncthing.dmg file and dragged and dropped the Syncthing.app to the Applications folder.
- I closed and dismounted the Syncthing.dmg
- I then launched Syncthing.app and proceeded as normal
Since doing the above, Syncthing has worked as expected without any problems.