add build checks to flake-health-checks

.github/workflows/flake-health-checks.yml

@@ -25,3 +25,22 @@ jobs:
       - uses: actions/checkout@v4
       - run: nix flake check --accept-flake-config
       - run: nix ./utils/attic-push.bash
+  build-checks:
+    name: "Build nix outputs"
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        os: [ubuntu-latest]
+    steps:
+      - uses: DeterminateSystems/nix-installer-action@main
+      - name: Setup Attic cache
+        uses: ryanccn/attic-action@v0
+        with:
+          endpoint: ${{ secrets.ATTIC_ENDPOINT }}
+          cache: ${{ secrets.ATTIC_CACHE }}
+          token: ${{ secrets.ATTIC_TOKEN }}
+          skip-push: "true"
+      - uses: actions/checkout@v4
+      - name: Build all outputs
+        run: nix run git+https://nayeonie.com/ahuston-0/flake-update-diff -- --build .
+      - run: nix ./utils/attic-push.bash