CAG based on which desktop you are on

I'd like to be able to activate a CAG based on which desktop I'm currently on. The basic idea is that I like to divide my different work types onto different desktops. On each desktop I have Slack, Firefox, Gmail, etc, with specific config for that work type. However, I want the same keyboard shortcut to work on each desktop. So, for example, on each desktop I want Alt+W to activate Firefox, but Firefox for that desktop.

The idea I had was to create different CAGs that activate based on which desktop I'm on. Is this possible? If not, is it a feature possibility?