Why do deleted emails reappear?

Can speak to iCloud.

The Others ( earthlink.net, and gmail.com ) suggest checking the Web Interface of each and make sure your setting are correct and or modified to function as expected.

https://support.apple.com/en-ca/HT202304

If you can’t send or receive email on your Mac

Who is one using as the Mail Server ? iCloud account, yahoo account, outlook account, g-mail account ?

Not talking about the Apple Mail Application - that is only the email Client.

From which of the three accounts is this occurring or from All.