Mail keeps randomly opening

I had this problem on Mojave where Mail kept popping open with a window randomly (while active but all windows closed). It was extremely obtrusive.

I recently did a clean install of Catalina on an external SSD (to boot from) - no migrating anything. The problem is continuing on the new system as well!

I leave Mail open and running in the background to see notifications - but once I'm done actively using it I always close the Finder window (not minimize) - the only thing related to Mail left is the active program in the dock. All notifications are on - but there is no option there for "automatically open" - yet somehow it just seems to randomly open while I'm working on other things.

In Catalina it appears as a new window in the background - which is a lot better than Mojave where it took over the main window completely and forced me out of the work I was doing.

Still it's not good - how to I make it stop?