As you probably know, gmail can be run as desktop app, rather than embedded in your browser. https://www.getmailflow.com/post/gmail-desktop-app
In this instance, it doesn't show on any of my Fusion Task Bars, besides the Primary monitor Task Bar.
Conversely, Google Calendar when it is also running as a desktop app... it does show on Fusion Task Bars. But when you pin it to a Fusion Task Bar, it pins as an instance of a Chrome browser, rather than as the desktop calendar app.
Obviously these are true desktop app, they are more like popped-out instances from the browser.
But would be very nice to see gmail on Fusion Task Bars when run in this way. It is almost a deal breaker.

Thanks for the reply. Video is a bit beyond my constraints right now. But here is a screenshot of gmail app open (with your forum email visible). Yet the gmail app is not in the taskbar. (Note again, this is not on the primary display task bar.)

That's the gmail app running on the desktop. I positioned it right above the task bar so that you could see it is running, yet the icon is not in the task bar on non-primary displays.