Outgoing mail not sent (gmail) w/ smtp

FWIW. IMAP (or POP3) is your email provider's incoming mail server. This is how the Mail app can retrieve messages that are sent to your email account. When you send messages, you use your provider's SMTP server to do so.

So, in your case, the issue appears to be with Google's (send mail) server. One, or more, of the following could be the reason(s):

1. The SMTP server settings in the Mail app is mis-configured. To check for the correct SMTP server settings for Gmail, I suggest that you enter your Gmail email address in the following Apple support article and it should provide them for you. For example, after I entered mine, I got smtp.gmail.com to be the server name and 587 for the secure port number to use. These may not necessarily be exactly the same for you, but most likely, they will be.
2. Your SMTP server user credentials are not correct. This should be your gmail address and password. You can test this by accessing your gmail account using a web browser, instead of the Mail app. If you can send a message from there, then you know your credentials are correct.
3. You enabled two-factor identification on your Google account. This may require that you use an app-specific password, instead of your normal password, to use with your gmail account in the Mail app. The following articles should help with this one:
   1. Using app-specific passwords - Apple Support
   2. Gmail: https://security.google.com/settings/security/apppasswords
   3. Let less secure apps use your account - Google
4. Gmail is having issues. This actually occurs more often than you think.

Same problem. I use two factor authentication with my google account and have for years. I have used Apple Mail successfully for years to access my gmail account. It has been set up with IMAP for incoming mail and SMTP for outgoing for years. Once before, it stopped working, several years ago, and I got an app specific password and that corrected the problem. Until last week. Now, a new app specific password doesn't help. The SMTP server remains offline. I've tried the app specific password, the regular password, over and over. No luck. Google also has a little page you're supposed to go to and sign in if you're having problems like this; that didn't work either. Google says that Apple Mail isn't secure enough; I doubt it! There is one option I haven't tried, which is to change the Google setting to allow less secure apps. I haven't done it because I need to conform to the HIPAA security rule for medical information. I'm reduced to using gmail on the web and using Apple Mail for my other accounts, but this is a pain. I'm hoping that Catalina fixes this.