feat: add workflow to sync base-action to claude-code-base-action repo (#299)

* feat: add workflow to sync base-action to claude-code-base-action repo

This workflow automatically mirrors the base-action directory to the
anthropics/claude-code-base-action repository whenever changes are
pushed to base-action files on the main branch.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

* feat: add automated release sync to claude-code-base-action

- Release workflow now creates matching releases in claude-code-base-action repo
- All release jobs now run in production environment
- Uses CLAUDE_CODE_BASE_ACTION_PAT for authentication

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

---------

Co-authored-by: Claude <noreply@anthropic.com>

.github/workflows/release.yml

@@ -12,6 +12,7 @@ on:
 jobs:
   create-release:
     runs-on: ubuntu-latest
+    environment: production
     permissions:
       contents: write
     outputs:
@@ -85,6 +86,7 @@ jobs:
     needs: create-release
     if: ${{ !inputs.dry_run }}
     runs-on: ubuntu-latest
+    environment: production
     permissions:
       contents: write
     steps:
@@ -115,6 +117,7 @@ jobs:
     needs: create-release
     if: ${{ !inputs.dry_run }}
     runs-on: ubuntu-latest
+    environment: production
     permissions:
       contents: write
     steps:
@@ -136,3 +139,49 @@ jobs:
           git push origin "$major_version" --force
 
           echo "Updated $major_version tag to point to $next_version"
+
+  release-base-action:
+    needs: create-release
+    if: ${{ !inputs.dry_run }}
+    runs-on: ubuntu-latest
+    environment: production
+    steps:
+      - name: Checkout base-action repo
+        uses: actions/checkout@v4
+        with:
+          repository: anthropics/claude-code-base-action
+          token: ${{ secrets.CLAUDE_CODE_BASE_ACTION_PAT }}
+          fetch-depth: 0
+
+      - name: Create and push tag
+        run: |
+          next_version="${{ needs.create-release.outputs.next_version }}"
+
+          git config user.name "github-actions[bot]"
+          git config user.email "github-actions[bot]@users.noreply.github.com"
+
+          # Create the version tag
+          git tag -a "$next_version" -m "Release $next_version - synced from claude-code-action"
+          git push origin "$next_version"
+
+          # Update the beta tag
+          git tag -fa beta -m "Update beta tag to ${next_version}"
+          git push origin beta --force
+
+      - name: Create GitHub release
+        env:
+          GH_TOKEN: ${{ secrets.CLAUDE_CODE_BASE_ACTION_PAT }}
+        run: |
+          next_version="${{ needs.create-release.outputs.next_version }}"
+
+          # Create the release
+          gh release create "$next_version" \
+            --repo anthropics/claude-code-base-action \
+            --title "$next_version" \
+            --notes "Release $next_version - synced from anthropics/claude-code-action" \
+            --latest=false
+
+          # Update beta release to be latest
+          gh release edit beta \
+            --repo anthropics/claude-code-base-action \
+            --latest