Gmail not working on Mac Mail I can't send mail, but working fine on Google app and my iPhone

Yes, Mac Mail in Ventura is rubbish. Worked fine in Monterey. some emails are not showing up at all and yet they are there on Googles web mail page.

Missed a few important replies over the last week, logging in and out makes no difference

Have you tried signing out and back in to that account? This may give it a kickstart.

Sometimes, "Take this account offline", then "Take this account online" helps too.