ci: fix some action issues

.github/workflows/website.yml

@@ -11,7 +11,7 @@ on:
     paths: ["website/**"]
 
 jobs:
-  format:
+  lint:
     name: Linting
     runs-on: ubuntu-latest
 
@@ -26,13 +26,19 @@ jobs:
           sparse-checkout: |
             website
 
+      - name: Install pnpm
+        uses: pnpm/action-setup@v4
+        with:
+          package_json_file: website/package.json
+
       - uses: actions/setup-node@v4
         with:
           node-version: 22
           cache: "pnpm"
+          cache-dependency-path: website/pnpm-lock.yaml
 
       - name: Install dependencies
-        run: pnpm install
+        run: pnpm install --frozen-lockfile
 
       - name: Run lint
         run: pnpm run lint