Cleanup dependencies (part 4) (#8468)

Follow-up to #8425 . Final part - adds the CI check.

Release Notes:
- N/A

.github/workflows/ci.yml

@@ -51,6 +51,9 @@ jobs:
       - name: Run style checks
         uses: ./.github/actions/check_style
 
+      - name: Check unused dependencies
+        uses: bnjbvr/cargo-machete@main
+
       - name: Ensure fresh merge
         shell: bash -euxo pipefail {0}
         run: |