There a couple of others for recording and video that don’t seem relevant.
I followed your steps with both of the above files as a base. The results are the same. The icon pins fine on the task manager but when I close the window and re-open by clicking on the pinned icon, it opens the main window on the server settings page. It does not load the session. It does group however.
If I find the desktop file again and double click it then the session loads and attaches to the pinned task manager icon and groups.