@uhrfru Welcome to the forum!
I’m not sure if I can say more than there is in the Help Sites… In essence, the sync function can sync TOTP “codes” between the dedicated (BW) authenticator app and the integrated authenticator of the Bitwarden password manager apps (and therefore, your Bitwarden account/vault).
(from the BW Help Sites – Sync Verification Codes | Bitwarden)
→ so it seems, there are some options, what you want to sync / which TOTP codes… i.e. it’s not automatically “sync all TOTP codes” (and I guess, what they call “local codes” in the text, are TOTP “codes” in the authenticator app, as they are stored locally on the device that has the authenticator app installed, when you don’t sync the authenticator app with the Bitwarden password manager/vault)
There is also a blog article about the Bitwarden authenticator app (with a Roadmap). It was published when the authenticator app was released. And I have a feeling, it might get an update now with the “sync function” released…: Bitwarden just launched a new authenticator app. Here’s what it means to users. | Bitwarden