docs: improve Fumadocs search and AI integration

.github/workflows/deployment-docs.yml

@@ -37,6 +37,10 @@ jobs:
         run: pnpm turbo build --filter=@homarr/docs
         env:
           CI: "true"
+      - name: Validate exported links and search
+        run: |
+          pnpm --filter @homarr/docs validate:links
+          pnpm --filter @homarr/docs verify:search
       - name: Setup Pages
         uses: actions/configure-pages@v6
       - name: Upload pages artifact

.github/workflows/docs-update-openapi.yml

@@ -32,7 +32,7 @@ jobs:
       - name: Commit updated spec
         uses: EndBug/add-and-commit@v10
         with:
-          add: "apps/docs/static/api/"
+          add: "apps/docs/public/api/"
           default_author: github_actor
           message: "chore(docs): update OpenAPI spec"
           push: true