My gmail is not working within Apple Mail.  It got where it reported offline status and stuff would get stuck in my outbox.  I tried deleting the account and putting it back and now it shows none of my mail.  With either explorer or safari, the app works fine.  Any other tricks I can use?
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Deleting your gmail account then re-adding it is definately a great step to take. It really should have solved it. So here's what I would do to work toward a solution.

1. Verify that I know my gmail password by going to safari or chrome: gmail.com, sign out if I'm signed in, then manually type the password. Once I'm certain of the password, move to step two.
2. Open system preferences: Internet Accounts and remove the gmail account from there. Quit system preference. Reopen mail.
3. Re-add the account. You'll be asked to sign in using Safari most likely as gmail now requires website authentication. It won't be a full fledged web page but instead, a smaller version that only shows your email and password area.
4. After you've attempted again to re-add the account, go back to gmail.com and look at your google account security settings. You should see an area for "authorized devices" and MacOS should be one. Gmail used to have a silly setting they turned off by default called "allow less secure devices". They considered MacOS a less secure device. That was their way of trying to get you to only use Chrome so they could better monetize advertising. If you see that setting, check "allow less secure devices".

If these steps don't solve it then there's a deeper issue that would most likely require a deeper dive into some support folders. Happy to assist remotely if needed.