Isn’t the value of two factor auth that it requires a physical device (your phone or computer) with the auth key to authenticate you? Then why don’t many two factor auth apps seem to support syncing? If it’s fine to do so, are there any open source cross platform apps that sync keys?
Nextcloud + Passman would do so.
One could argue that this is against the idea of 2FA. In case you lose your device, you should simply use another with different token and delete the validity of the lost one.
Additionally, as 2FA is supposed to add an extra layer of security, having 2FA token and passwords stored in the same db is also not the best idea in that regard.