Old sent mail appearing in inbox

Are you sure it's not the "follow up" feature that's been added? You'll see a small follow-up icon next to the mail contents

From Apple support

Get reminded to follow up on emails with no response

If you send a message and don’t receive a response in 3 days, the sent email automatically resurfaces to the top of your inbox to help you remember to follow up.

• • To ignore a follow-up suggestion, swipe right on the message in the message list.
  • To turn this feature on or off, choose Mail > Settings, click General, then select or deselect the tickbox next to “Enable message follow up suggestions”.

Centime wrote:

Why do I keep receiving mail I sent in my inbox?

Old issue, new issue, what changed?

Verify your Mail>Settings....(?)

ref: Mail User Guide for Mac