Add linting to frontend (#4341)

# Description of Changes
There's no current linter running over our TypeScript code, which means
we've got a bunch of dead code and other code smells around with nothing
notifying us. This PR adds ESLint with the typescript-eslint plugin and
enables the recommended settings as a starting point for us.

I've disabled all of the failing rules for the scope of this PR, just to
get linting running without causing a massive diff. I'll follow up with
future PRs that enable the failing rules one by one.

Also updates our version of TypeScript, which introduces a new type
error in the code (which I've had to fix)

.github/workflows/build.yml

@@ -147,6 +147,8 @@ jobs:
           cache-dependency-path: frontend/package-lock.json
       - name: Install frontend dependencies
         run: cd frontend && npm ci
+      - name: Lint frontend
+        run: cd frontend && npm run lint
       - name: Build frontend
         run: cd frontend && npm run build
       - name: Run frontend tests