[Chore]: refactor test dependencies

[jsjoeio]

Pointed out by @code-asher, we should be separating our dependencies correctly. Right now the yarn test:integration relies on both dependencies at the root and in /test.

We need to move any test dependencies to /test/package.json (i.e. jest and typescript).

More discussion: https://github.com/coder/code-server/pull/5275#discussion_r905234769