No insights, I'm afraid, other than, as with others' experiences, my Apple Mail began to periodically appear on my desktop unprompted by me. This problem coincided with my having just added a Gmail account. I subsequently searched online regarding the problem and eventually followed some instructions (via user questions/feedback on Apple's site, if I recall correctly) regarding Google account settings (amending these) but to no avail. I do think it's a Google thing – Google 'just checking in'. Not impressed.
I'm using Mojave on a 2015 MacBook Air.
Edit: I just remembered I'd copied this to assist me (when I did my online search about the Mail problem as mentioned above):
Begins:
Problem
The problem seems to be with Google Calendar Notification Settings. I had configured Gmail and my Google Calendar on the the Mac calendar app was disabled and yet I faced this issue
Solution:
Login into
https://calendar.google.com > Settings > Calendar link > Notifications. Edit Notifications then unselect email from the drop down. Save it and then quit and re-open mail app.
Credit must go to the original poster for posting the solution, link is below:
Refer:
https://discussions.apple.com/thread/7271461
Ends
Maybe it'll work for you?