Make popped out chat window handle resize significantly better

Group of responsiveness cleanups for tear-out chat window; an updated, reviewed, and tested version of PR 190.

I created a new branch off of master, and cherry-picked @n1k0's original fix.  This fix makes a number of things better and more responsive, at the minor cost of making the text history scrollbar thumb extend _under_ the text input line.

I re-applied the review tweaks we did, this time one fix per commit, and ran all the tests.  Ultimately, I ended up leaving out:

* the stuff where we tried to avoid having both 65vh and 35vh.  This is the thing that never quite worked right.
* the z-index tweaks, as they would have left the file in a somewhat inconsistent state
* devel/chat-layout.html, as this felt super fragile and I _think_ we should be able to limp along without that given one of the hidden prefs until we templatize the chat window separately.  I'm open to being convinced otherwise, however.