Keep 'change extensions' dialog up while processing changes before quitting

For #6257. @dangoor - maybe this would be good for you to look at since I think you did the original update flow on quit.

The main change is just to make it so the dialog doesn't autodismiss when buttons are clicked, so we can keep it open and just disable the buttons/change the message while the changes are being applied.

Worth looking at the diffs with `?w=1` in ExtensionManagerDialog.js since that makes the actual changes more obvious.