Who on earth sends their PGP key to the email client?

Yes, I know there are people who do it.

The right way to use PGP, of course: write your message on Notepad, then select and copy all. Then encrypt the clipboard with PGP and paste that encrypted contents on your email window. If you have attachments, encrypt them first on your computer, then attach them to your email message.

The email client has nothing to do with this process except for sending your gibberish message.