As suggested, to send mail, you need a mail server. The typical interface is SMTP, but with outlook you can also use the graph api.
I would not recommend System.Net.Mail As it is no longer maintained, and does not support modern authentication (can not be used with outlook.com).
if deploying to azure webapp, be sure your SMTP server is accessible from the internet. You also will not be able to use default credentials as you don’t control the service app account.
you don’t says the mail server you are using, but to use the oauth user account, it must support your oauth users.