Passwords App deleted my 2FA profile

I had two entries for logging in to a site: one with my username and password, and another with my username and 2FA code. The Password app deleted the one with the 2FA code, leaving only the username/password entry. The code is also not appearing in the bin or on the other devices, which were synced via the magic of an iCloud Keychain.

So now - I have my login credentials - but no way to actually log in.

The Big Question: Is there any way to recover the missing 2FA code? I cannot delete my 2FA profile in the target site because they are requesting me to contact Apple support to regain access to the lost codes.