Not sure what the Bitwarden TOTP app is, totp is build into the default clients.
I’ll also confirm that 2fa with beehaw at least is working for me. Vaultwarden shouldn’t make a difference, it’s just the data host, your client is the one decoding and then generating the otp.
My advice, you shouldn’t have to add anything. Copy the totp link from your lemmy instance and paste the entire link into the Authenticator Key field in the bitwarden entry. The link should start with otpauth://totp/. Don’t remove anything from the link, it’ll work as is.
If you’re finding it’s still not giving you the correct code, the only other thing that comes to mind is to make sure your device’s time is synced and accurate. TOTP codes are time sensitive, and if the device’s time is desynced, you will get incorrect codes generated.