I just brought my laptop up to date from High Sierra to Mojave, and my mail is gone. I use IMAP and Gsuite. I have good backups (I think). New emails are being received correctly, and I can send correctly. What next?
If you use IMAP, that should mean that just because the local copies are deleted, the server should still have them.
Have you logged in via the website to check and see if it’s there?
Yes, I have, and no, they are not 
Remove the account via System Preferences
internet accounts
Empty the ~/Library Mail folder
Restart your Mac
Add the account back via the System preferences > Internet accounts pane
did you by any chance move them from the server to a local email folder?
In that case the server would be empty indeed.
Did you make a backup or clone before the upgrade?
Time Machine bailed me out, so I was able to restore the lost data. I wish I understood what went wrong, though, so I don’t make the same mistake again.
Check if the folders with email were stored “on my Mac” vs under the IMAP account.
I save emails on my Mac so those were still there, but nothing else.