Just to make sure we are on the same version. I am on Edge Version 119.0.2151.72 and Windows 11 v 23H2 (OS Build 22631.2715).
Do know that when I tested on my system The app icon did change to black square for a short moment and it change back to its original icon after that. I tested on Youtube and another local shoping page. Please share a page that you see an issue so I can verify it on my system.
Added note: I am also on Start11 Enhanced taskbar.
Stardock Community Assistant
max, apple tv, the roku channel, disney +
It's not just Edge in chrome it just displays a generic chrome icon. It's not displaying the installed Web app icon for any. Although youtube tv displays the edge blank square behaviour in chrome. It's truly all over the board. The only one I have seen work as you described is Peacock it loads very slow but finally loads the icon in edge. This is not ideal and is not working in my opinion.
Please see my post from two weeks ago for a screenshots. As someone who uses a lot of these installed apps with these browsers. This makes this enhanced taskbar completely unusable you can't at a glance what apps are running.
Again enhanced taskbar has always exhibited this behavior for me since the inception of the feature. start11 v1 and v2 both did this for me.