[STREAM-32] Update dependencies

[hjon]

Quite a bit changed between changing the linter from TSLint -> ESLint and adding Prettier. Looking at the individual commits for each of those might be the easiest way to see how they affected things.

Some of the config changed for Jest (and I decided to remove some things we weren't using).

I also removed a few scripts and badges that don't seem to be used anymore.

In all cases, let me know if I trimmed too much, we want to use different options (or more or fewer), we want to fix linting errors differently, etc.