At work we’re all Google. I have not seen the behavior you describe at work with Mojave and Mail.app or with iOS 12.4.whatever and Mail there. But we’ve not been switched to 2FA yet. Do you see the same behavior if you use the Gmail web interface?
Still watching Outbox in Apple Mail just sit there for hours this AM. I plan to delete/remove that account from Apple Mail and then add back. Hopefully that will resolve it but I’m not optimistic.