[yjftsjthsd-h]

It's not just a GNOME thing, but it might not be that cross-platform. On Linux, there's a firefox.desktop file that describes the application to your DE/launcher, and it looks like this on my box:

    [Desktop Entry]
    Actions=new-private-window;new-window;profile-manager-window
    Categories=Network;WebBrowser
    Exec=firefox --name firefox %U
    
    ---snip---
    
    [Desktop Action profile-manager-window]
    Exec=firefox --ProfileManager
    Name=Profile Manager

So that'll work on anything that uses https://specifications.freedesktop.org/desktop-entry-spec/de... and there could be parallel features for Windows/Mac, but there also might not be or Firefox might not implement them.