Automatically trigger build workflow after sync update

When update.yml detects new Ruby versions and pushes a commit,
dispatch build.yml to rebuild Docker images automatically.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: hsbt

.github/workflows/build.yml

@@ -2,6 +2,8 @@ name: Build Docker image
 
 on:
   workflow_dispatch:
+  repository_dispatch:
+    types: [build]
 
 permissions:
   contents: read

.github/workflows/update.yml

@@ -12,11 +12,22 @@ jobs:
       - uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6.0.2
       - run: rake sync
       - name: commit and push
+        id: commit
         run: |
           git config user.name "GitHub Actions Bot"
           git config user.email "github-actions[bot]@users.noreply.github.com"
           git add .
-          git commit -m "rake sync"
-          git push
+          if git diff --cached --quiet; then
+            echo "updated=false" >> "$GITHUB_OUTPUT"
+          else
+            git commit -m "rake sync"
+            git push
+            echo "updated=true" >> "$GITHUB_OUTPUT"
+          fi
         env:
           GITHUB_TOKEN: ${{ secrets.MATZBOT_AUTO_UPDATE_TOKEN }}
+      - name: dispatch build
+        if: steps.commit.outputs.updated == 'true'
+        run: gh workflow run build.yml
+        env:
+          GH_TOKEN: ${{ secrets.MATZBOT_AUTO_UPDATE_TOKEN }}