ci: add nix flake check to ci

Author: andrew-scott-fischer

.github/workflows/format.yaml

@@ -9,9 +9,20 @@ concurrency:
   cancel-in-progress: true
 
 jobs:
-  check:
+  nix-flake-check:
+    name: Nix Flake Check
     runs-on: ubuntu-latest
+    steps:
+      - name: Install Nix
+        uses: DeterminateSystems/nix-installer-action@de22e16c4711fca50c816cc9081563429d1cf563 # v10
+
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - run: nix flake check
 
+  check:
+    runs-on: ubuntu-latest
     steps:
       - name: Checkout
         uses: actions/checkout@v4