Two different kinds of proof
A password is something you know. A separate authenticator or security key can add proof tied to something you possess. The protection depends on how the account and the second factor are set up.
The code and the setup key are different
The short code is what you enter when signing in. The setup key is the longer secret used to produce codes. Sharing the key gives away much more than sharing a single expired code.
Choose a method your account supports
Follow the service’s enrollment instructions. Keep its recovery options accessible, and consider security keys or passkeys where available. A TOTP code can still be stolen by a convincing phishing page.
Where this website fits
The tools here help inspect setup data and calculate codes. They do not enroll your account, recover access, or replace a service’s recovery process.