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?
Ente Auth
F-Droid: https://f-droid.org/packages/io.ente.auth/
You can easily self-host it:
https://help.ente.io/self-hosting
It’s considered bad form to do what you’re asking but most 2fa apps have a backup restore scheme now. Is that enough?
A physical token only authenticates itself as “something you have” if there’s no way to extract the key from it. In practice non-hardcore deployments usually have a backup procedure but in principle, if you want multiple tokens, they should have separate keys. What you’re asking in simplest form involves storing the key on a server where it can potentially spill in a server breach or the like. If the key protects something very valuable, that can be dangerous. If it’s for your old Reddit account, you might decide to do it anyway.
You can use KeePassXC (with a dedicated vault or not), synced by another mean (Nextcloud, Syncthing, Git, etc.).
You can create TOTP for login records in bitwarden and sync it of course. But make sure you protect your wallet key with additional security methods.
There is the completely open source https://standardnotes.com/ which would support that via their syncing and the authenticator note type.
Unfortunately it does not look like their free plan allows you to use that note type. So could also host it yourself though (and pay for the premium token their or hack it out - it’s foss). Have never done that myself though
