I had this issues when I enabled WAYLAND for ms-edge using the ~/.config/microsoft-edge-stable-flags.conf
file
--enable-features=WebRTCPipeWireCapturer
--enable-features=UseOzonePlatform
--ozone-platform=wayland
I was able to find the WMClass for the “App” after opening it using this
unix[dot]stackexchange[dot]com/questions/362731/how-to-identify-window-by-clicking-in-wayland
Once I knew that, all I had to do was rename the .desktop file based on it. Which was just adding _
to the name e.g.
mv msedge-hpfldicfbfomlpcikngkocigghgafkph-Default.desktop msedge-_hpfldicfbfomlpcikngkocigghgafkph-Default.desktop
^^^
And I got the “Icons” like how it was before.