feat: try deploying the page on GitHub Actions

this never works on the first try

.github/workflows/deploy.yml

@@ -0,0 +1,81 @@
+name: Deploy Next.js site to Pages
+
+on:
+  push:
+    branches: ["main"]
+  workflow_dispatch:
+
+permissions:
+  contents: read
+  pages: write
+  id-token: write
+
+concurrency:
+  group: "pages"
+  cancel-in-progress: false
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Detect package manager
+        id: detect-package-manager
+        working-directory: ./demo
+        run: |
+          if [ -f "yarn.lock" ]; then
+            echo "manager=yarn" >> $GITHUB_OUTPUT
+            echo "command=install" >> $GITHUB_OUTPUT
+            echo "runner=yarn" >> $GITHUB_OUTPUT
+          elif [ -f "package.json" ]; then
+            echo "manager=npm" >> $GITHUB_OUTPUT
+            echo "command=ci" >> $GITHUB_OUTPUT
+            echo "runner=npx --no-install" >> $GITHUB_OUTPUT
+          else
+            echo "Unable to determine package manager"
+            exit 1
+          fi
+
+      - name: Setup Node
+        uses: actions/setup-node@v4
+        with:
+          node-version: "lts/*"
+          cache: ${{ steps.detect-package-manager.outputs.manager }}
+          cache-dependency-path: ./demo/package-lock.json
+
+      - name: Setup Pages
+        uses: actions/configure-pages@v4
+
+      - name: Restore cache
+        uses: actions/cache@v4
+        with:
+          path: ./demo/.next/cache
+          key: ${{ runner.os }}-nextjs-${{ hashFiles('demo/**/package-lock.json', 'demo/**/yarn.lock') }}-${{ hashFiles('demo/**.js', 'demo/**.jsx', 'demo/**.ts', 'demo/**.tsx') }}
+          restore-keys: |
+            ${{ runner.os }}-nextjs-${{ hashFiles('demo/**/package-lock.json', 'demo/**/yarn.lock') }}-
+
+      - name: Install dependencies
+        working-directory: ./demo
+        run: ${{ steps.detect-package-manager.outputs.manager }} ${{ steps.detect-package-manager.outputs.command }}
+
+      - name: Build with Next.js
+        working-directory: ./demo
+        run: ${{ steps.detect-package-manager.outputs.runner }} next build
+
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v3
+        with:
+          path: ./demo/out
+
+  deploy:
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    runs-on: ubuntu-latest
+    needs: build
+    steps:
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4