Try a different way to combine site and firmware

.github/workflows/publish.yml

@@ -13,7 +13,7 @@ on:
     types: [published]
 
 jobs:
-  build:
+  build-firmware:
     name: Build Firmware
     uses: esphome/workflows/.github/workflows/build.yml@main
     with:
@@ -22,37 +22,54 @@ jobs:
         project-template-esp32-c3.factory.yaml
         project-template-esp32-s3.factory.yaml
       esphome-version: 2024.7.3
-      combined-name: project-template
+      combined-name: firmware
       release-summary: ${{ github.event_name == 'release' && github.event.release.body || '' }}
       release-url: ${{ github.event_name == 'release' && github.event.release.html_url || '' }}
       release-version: ${{ (github.event_name == 'release' && github.event.release.tag_name) || (github.event_name == 'workflow_dispatch' && inputs.version) || '' }}
 
+  build-site:
+    name: Build Site
+    runs-on: ubuntu-latest
+    steps:
+      - name: Build
+        uses: actions/[email protected]
+        with:
+          source: ./static
+          destination: ./output
+      - name: Upload
+        uses: actions/[email protected]
+        with:
+          name: site
+          path: output
+
   publish:
     name: Publish to GitHub Pages
     if: github.event_name == 'release' || (github.event_name == 'workflow_dispatch' && github.ref == 'refs/heads/main')
     runs-on: ubuntu-latest
-    needs: [build]
+    needs:
+      - build-firmware
+      - build-site
     permissions:
       pages: write
       id-token: write
     environment:
       name: github-pages
       url: ${{ steps.deployment.outputs.page_url }}
     steps:
-      - uses: actions/[email protected]
       - uses: actions/[email protected]
         with:
-          name: project-template
-          path: files
-
-      - name: Build
-        uses: actions/[email protected]
-        with:
-          source: ./static
-          destination: ./output
+          name: firmware
+          path: firmware
 
       - name: Copy firmware and manifest
-        run: cp -r files/${{ needs.build.outputs.version }}/* output/
+        run: |-
+          mkdir -p output/firmware
+          cp -r firmware/${{ needs.build-firmware.outputs.version }}/* output/firmware/
+
+      - uses: actions/[email protected]
+        with:
+          name: site
+          path: output
 
       - uses: actions/[email protected]
         with: