For me, the app icon only shows in the preview window. It doesn't show in the Windows 11 task manager.
With that said, you can goto the URL opera://extensions turn on developer mode and click "details" for a mod with an app icon to get its ID. Then, goto the URL opera://about, take note of the "profile" path, browse to the "Extensions" folder in the profile folder, go into that ID folder, go into the version folder and you'll see the app icon file (in an "app icon" folder for example).
In the mod I tested with, the app icon is a png file which isn't compatible with the taskbar. But, I imagine you could convert it to an ico file. Then, you can right-click on Opera GX's taskbar button, right-click on "Opera GX Browser", goto "Properties", click "change icon" on the "General" tab and point it to the ico version of the app icon. That might work. Just note that you might have to open the Windows Task Manager, select the Windows Explorer process on the Processes tab and restart Windows Explorer to see the change. But, it's something you can try if you really really want it.
