How make Mac OS mail Connection Doctor forget older accounts

I have created a number of "internet" accounts for mail in Mac OS, but for various reasons they didn't work, and I deleted them from the listings in the preferences, and of course they therefore don't appear in the Mac OS Mail app either. In fact, there are now zero accounts registered with mail abilities and zero appearing in my Mail app.

BUT, if I go to Mail, and choose Connection Doctor, it still scans those old email accounts to see if they can connect or not!

So it is clearly "retaining" those old accounts... and their credentials!! (because they are actually giving green lights for successful connection!) ...

How do I get it to forget those old accounts? Cleanse that oddly cached account info?

Thanks!