tab groups: make the "window button" in the taskbar have the tab group's name

[j-pee]

hi, 

It would be great to see the group title over the "window button" in the "taskbar" (in linux terms)...

Scenarios: 

• in a window, all tabs belong to a group... 
• in a window tab is in focus which belongs to a group

in both cases it would make sense if the window button inherited the tab group's title

Peter

* * * * * tank you for developing Firefox !!! * * * *

[Jon]

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[FacesOfMu]

I just switched to FF and would really love both of these changes, too. I came here to ask exactly for both of these, the taskbar indicator for which window is which group, and making it so that every new tab opened in that window is added to the group (no needing to manually add it or create it from between two tabs in the group).
Once I've got my groups created, I just need my workflow to go smoother between windows and within the windows based on their groups.