@Moskito With “Bitwarden” I guess you mean the integrated TOTP authenticator. Yeah, you can store your Bitwarden account TOTP seed in Bitwarden, but of course not solely then.
I personally would try to change to FIDO2 WebAuthn as Bitwarden-account-2FA… Maybe your phone, Windows Hello or something is able to do that… FIDO2 WebAuthn is more secure and not phishable. And you don’t need a 2FA app then…
BTW: Note your 2FA recovery code for your Bitwarden account and store it on an emergency sheet, if not already done… And a backup of all your TOTP seed codes wouldn’t be a bad idea either - though, if you have them in your Bitwarden vault, regular backups/exports of your vault would be enough.