feat: use cachix nix-install-action

.github/workflows/flake-update.yml

@@ -1,8 +1,8 @@
 name: flake-update
 on:
-  workflow_dispatch: 
+  workflow_dispatch:
   schedule:
-    - cron: '0 5 * * 0' 
+    - cron: '0 5 * * 0'
 
 jobs:
   lockfile:
@@ -11,11 +11,10 @@ jobs:
       - name: Checkout repository
         uses: actions/checkout@v4.2.2
       - name: Install Nix
-        uses: DeterminateSystems/nix-installer-action@v17
+      - uses: cachix/install-nix-action@v31
       - name: Update flake lock
         run : |
           git config --local user.email "github-actions[bot]@users.noreply.github.com"
           git config --local user.name "github-actions[bot]"
           nix flake update --commit-lock-file
           git push origin HEAD:${{ github.ref_name }}
-