For some of the UI/product work I'm thinking about for Home and for Firefox, it would be useful for the client to be able to know what app tabs are open on other instances of Firefox.

If the information is there in the records for each tab, then this shouldn't be too hard to do. Marking "good first bug" until proved otherwise :)

I'm not sure how this should tie into our general direction for Tabs From Other Computers. This feature isn't very discoverable right now on desktop, mostly because it's (a) shyte and (b) mostly useful for mobile. I think the best improvement we can do on desktop is to tie this information into awesomebar results (bug 662664). Faaborg's long term goal is to factor it into Panorama (bug 652040) which should then also include a story for app tabs, for sure. So the question is, are you looking for a short-term solution, Madhava? If so, what should the UX be? Or are you purely trying to get desktop Firefox to sync this information to the cloud so you can exploit it in Fennec? Removing the good first bug status for now since I don't think it's at all clear what we want to do here.

In the ideal world the user would have only one set of app tabs (and they wouldn't have different sets on every computer). Since they do have different sets on every desktop computer, could we just add support on mobile by aggregating all of them for now?

Maybe it could also help for disappearing app tabs (see bug 587400).

We updated the synced tabs experience, and I'm closing out these old bugs to update the previous experience.