refactor: publish.yml dispatches deploy-website instead of workflow_run

Co-authored-by: aaronpowell <434140+aaronpowell@users.noreply.github.com>

.github/workflows/publish.yml

@@ -10,6 +10,7 @@ concurrency:
 
 permissions:
   contents: write
+  actions: write
 
 jobs:
   publish:
@@ -52,3 +53,8 @@ jobs:
           git add -f plugins/*/agents/ plugins/*/skills/
           git commit -m "chore: publish from staged" --allow-empty
           git push origin HEAD:main --force
+
+      - name: Dispatch website deployment
+        run: gh workflow run deploy-website.yml --ref main
+        env:
+          GH_TOKEN: ${{ github.token }}