I am using task manager view, never group icons.
I have created desktop shortcuts for web apps such as Google docs.
When I open such a shortcut, the icon when it is on the panel turns into a generic Chrome icon, instead of the unique Google docs icon that shows on the shortcut.

I am on Manjaro with KDE desktop. I didn't see this issue with Kubuntu.

Operating System: Manjaro Linux
KDE Plasma Version: 5.16.2
KDE Frameworks Version: 5.59.0
Qt Version: 5.12.4
Kernel Version: 5.1.15-1-MANJARO
OS Type: 64-bit
Processors: 4 × Intel® Core™ i5-6500 CPU @ 3.20GHz
Memory: 7.7 GiB of RAM