docs: integrate search functionality with new SearchDialog component

- Added a new SearchDialog component to enhance user experience for searching documentation.
- Updated the layout to include the SearchDialog within the RootProvider for improved accessibility.
- Enhanced the search API to support tag filtering based on the first slug, allowing for more refined search results.

apps/docs/app/api/search/route.ts

@@ -1,7 +1,21 @@
 import { source } from '@/lib/source';
 import { createFromSource } from 'fumadocs-core/search/server';
+import type { InferPageType } from 'fumadocs-core/source';
 
 export const { GET } = createFromSource(source, {
   // https://docs.orama.com/docs/orama-js/supported-languages
   language: 'english',
+  // Configure tag filter based on the first slug (core, cli, api)
+  buildIndex(page: InferPageType<typeof source>) {
+    const tag = page.slugs[0] || 'all';
+    return {
+      title: page.data.title,
+      description: page.data.description,
+      url: page.url,
+      id: page.url,
+      structuredData: page.data.structuredData,
+      // Assign tag based on the first slug (core, cli, api)
+      tag,
+    } as any;
+  },
 });