Convert UI to ReactJS

The UI should look almost identical to how it did before, but with a couple fewer bugs and a few more features.

The main new feature is that webdiff now shows the full list of files, which can be collapsed to a dropdown if desired.
I'd suggest conditionally setting `display: none` on the `div`. In this case it doesn't matter much, but it's a lot cheaper to change a class or set `display: none` than adding and removing DOM elements. It also may be a little clearer than returning an empty span. Totally a nitpick, but just FYI.