switch to using determinate systems gha for ci

.github/workflows/deploy.yml

@@ -15,25 +15,13 @@ jobs:
       uses: actions/checkout@v4
 
     - name: Install Nix
-      uses: cachix/install-nix-action@v31
-      with:
-        nix_path: nixpkgs=channel:nixos-unstable
+      uses: DeterminateSystems/determinate-nix-action@v3
 
-    - name: Setup Nix store cache
-      uses: actions/cache@v4
-      with:
-        path: /nix/store
-        key: ${{ runner.os }}-nix-store-${{ hashFiles('**/flake.lock') }}
-        restore-keys: |
-          ${{ runner.os }}-nix-store-
+    - name: Setup FlakeHub Cache
+      uses: DeterminateSystems/flakehub-cache-action@main
 
-    - name: Cache flake inputs
-      uses: actions/cache@v4
-      with:
-        path: ~/.cache/nix
-        key: ${{ runner.os }}-nix-flake-${{ hashFiles('**/flake.lock') }}
-        restore-keys: |
-          ${{ runner.os }}-nix-flake-
+    - name: Check Nix flake
+      uses: DeterminateSystems/nix-flake-checker-action@main
 
     - name: Build site (pull request)
       if: github.event_name == 'pull_request'