This makes it identical to a password from a theoretical perspective. There's really no difference between a TOTP secret that you keep in a TOTP app and haven't memorized, and a password you keep in your password manager and also haven't memorized. Both are "something you know", and nothing else.
You're correct that leaking a temporary code from a single login attempt doesn't compromise the TOTP secret. That is an artifact of the login process, not of whether the mechanism is labeled "2FA" or "password". You can do the same thing while calling the secret a password: https://en.wikipedia.org/wiki/Secure_Remote_Password_protoco...