Basically the problem this solves is cases where you had Tweak Tool open at the same time as extensions.gnome.org and you installed or removed something from e.g.o. With this patch the "Extensions" pane is updated with the new extension (or without the removed extension).
There's some XXX comments in there I still need to address, but I wanted to open this to see if the general approach looks OK. Also, any advice to solve the need to sleep would be much appreciated - it's an ugly hack but I had to put it in there since apparently during extension installs (not removals) there's a race between the inotify notification and GNOME Shell actually registering the extension as installed. Without the sleep the call to list extensions does not include the new extension.