fix(deploy-static-site): inline tool cache push to fix HOME expansion in with block

deploy-static-site/action.yaml

@@ -55,11 +55,15 @@ runs:
 
     - name: Cache installed tools
       if: env.NIX_SIGNING_KEY != ''
-      uses: https://git.toph.so/toph/ci-actions/push-nix-cache@main
-      with:
-        store-path: ${{ env.HOME }}/.nix-profile
-        s3-endpoint: ${{ inputs.s3-endpoint }}
-        s3-bucket: ${{ inputs.s3-bucket }}
+      shell: bash
+      run: |
+        echo "${NIX_SIGNING_KEY}" > /tmp/nix-key
+        nix store sign -k /tmp/nix-key --recursive "$HOME/.nix-profile"
+        rm /tmp/nix-key
+        nix copy --to "file:///tmp/nix-tools-cache" "$HOME/.nix-profile"
+        aws s3 sync /tmp/nix-tools-cache \
+          "s3://${{ inputs.s3-bucket }}" \
+          --endpoint-url "${{ inputs.s3-endpoint }}"
 
     - name: Build site
       shell: bash