Update project typecheck configuration so that typechecking may be
additionally applied to the `dev-server` area of the project. This helps
for typechecking usage of components in the "UI Playground" app.

* Add `tsconfig.json` for `dev-server` area of project
* Add "project references" at root level
  See https://www.typescriptlang.org/docs/handbook/project-references.html
* Update `package.json` `typecheck` script