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?
You can use KeePassXC (with a dedicated vault or not), synced by another mean (Nextcloud, Syncthing, Git, etc.).