I purposely went with google Authenticator because of the syncing feature. I didn’t want to be locked out if I lost my phone.
Also because I have never heard of Syncthing before
Discussion
Gotcha. It's good stuff.
https://www.privacyguides.org/en/file-sharing/#syncthing-p2p
Another way is to have a old phone and backup your code or print the qr backup code and put it in a safe.