Convert JavaScript to TypeScript

[louh]

Following up from #129, it's become pretty evident that the props being passed through nested components causes issues, and we could both improve that and make this entire repo easier to work with by converting it to TypeScript.

After some initial experiment and research, it does feel like the porting process is reasonably trivial. The biggest issues so far will be things that are actual bugs and will need to be Actually Fixed, and things that are done Sort Of Weirdly and need some reverse engineering to property type.

Anyway it's in progress.