Hello bbohm21,
Are you able to manually delete the drafts in the Drafts folder using the Delete option in the toolbar or Edit > Delete? If so, do they stay gone when you do that or reappear? Also, do the emails initially clear out of the Drafts folder and come back later when you send an email or do they never delete, even momentarily?
As far as troubleshooting this behavior goes, we advise that you restart your Mac (Shut down or restart your Mac) and make sure it's fully updated (Update macOS on Mac). Once those are done, please test this issue.
If the issue persists, continue by testing to see when this behavior occurs. First, put your Mac into safe mode and test. Booting into safe mode will disable any startup and login items from automatically opening, which can help us to isolate the source of the issue further. When you do this, you’ll see some unusual behavior from the display; this is to be expected. Please follow the steps in this article: How to use safe mode on your Mac.
Next, let's see if this behavior persists in a second user account on your Mac. Testing in a new user will determine if you have a system-wide issue or if it's user-specific. Please follow these steps to make a test account that can be deleted later: Change Users & Groups settings on Mac.
Let us know how this goes, please. Thanks and take care.