TMflyfisher wrote:
Deleted emails remain in the list. I have to shutdown and restart Email to "unlist" them. Usually only messages from bulk mailing services
You can try disabling the account, the re-enable and compare your results.
For problem accounts the go to way to sort things out is to delete the account(s) from the Mail.app, then add it back.
Remove email accounts in Mail on Mac
Remove email accounts in Mail on Mac - Apple Support
Add email accounts in Mail on Mac - Apple Support
Add email accounts in Mail on Mac - Apple Support
Note—
IMAP accounts stay on the server, so no local loss, when you re-sync
POP accounts download and remove from the server—therefor save your inbox/sent box if you want them
“On My Mac" is just that, local folders you created and moved mail into. So no loss