The details of how to open a new window in Manager desktop varies with operating system. On a mac you
In all cases what you are actually trying to find out is what port number is used for the current invocation of Manager (as all other parts of the URL are constant).
It is possible an appimage has greater process isolation than all other implementation. To prove that we would need to find the linux desktop URL and show it doesn’t work, yet the old linux desktop implementation it does work