I maintain a window management addon and a user has asked if support for OS workspace awareness is possible (Desktops in Windows, Spaces in Mac, etc). Basically, could an extension find out which OS workspace a particular browser window is in? Via native messaging perhaps?
There aren’t extension APIs for this kind of thing. I expect that native applications can retrieve this information somehow, but I don’t know any of the details there. So, yes, in theory a native messaging-based approach would work.