I was with you until the word "app" then you threw me off a bit. I'm unsure what you had done.
What are you using to send/forward email...webmail or a local email client on your computer?
Two-Factor Authentication (2FA) and OAuth2 are different security standards.
2FA is for an email account on a server...such Cox webmail, Yahoo, Gmail, etc...to verify the person logging into your account is actually you. In addition to the correct username and password, the server wants another factor: token, fingerprint scan, security answer, security code. After you successfully log in via 2FA, this standard wouldn't effect sending/forwarding email. It's just to login.
OAuth2 is for adding said account to an email-client program...such as Outlook, T-bird, Aqua Mail....and doesn't use any of the credentials mentioned above. If you configure your client, OAuth2 uses a third-party website to request a temporary access token from Cox.
If you’re using 2FA, it wouldn't apply to an app...unless the app is a browser.