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. 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. I've tried the app specific password, the regular password, over and over.
Now, a new app specific password doesn't help. Once before, it stopped working, several years ago, and I got an app specific password and that corrected the problem. It has been set up with IMAP for incoming mail and SMTP for outgoing for years. I have used Apple Mail successfully for years to access my gmail account. I use two factor authentication with my google account and have for years. This actually occurs more often than you think.
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. The SMTP server settings in the Mail app is mis-configured.
One, or more, of the following could be the reason(s): So, in your case, the issue appears to be with Google's (send mail) server. When you send messages, you use your provider's SMTP server to do so. This is how the Mail app can retrieve messages that are sent to your email account. IMAP (or POP3) is your email provider's incoming mail server.