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/components/SearchDialog.tsx

@@ -0,0 +1,54 @@
+'use client';
+
+import {
+  SearchDialog,
+  SearchDialogClose,
+  SearchDialogContent,
+  SearchDialogFooter,
+  SearchDialogHeader,
+  SearchDialogIcon,
+  SearchDialogInput,
+  SearchDialogList,
+  SearchDialogOverlay,
+  TagsList,
+  TagsListItem,
+  type SharedProps,
+} from 'fumadocs-ui/components/dialog/search';
+import { useDocsSearch } from 'fumadocs-core/search/client';
+import { useState } from 'react';
+
+export default function CustomSearchDialog(props: SharedProps) {
+  const [tag, setTag] = useState<string | undefined>('all');
+  // When tag is "all", don't filter by tag (pass undefined)
+  const { search, setSearch, query } = useDocsSearch({
+    type: 'fetch',
+    tag: tag === 'all' ? undefined : tag,
+  });
+
+  return (
+    <SearchDialog
+      search={search}
+      onSearchChange={setSearch}
+      isLoading={query.isLoading}
+      {...props}
+    >
+      <SearchDialogOverlay />
+      <SearchDialogContent>
+        <SearchDialogHeader>
+          <SearchDialogIcon />
+          <SearchDialogInput />
+          <SearchDialogClose />
+        </SearchDialogHeader>
+        <SearchDialogList items={query.data !== 'empty' ? query.data : null} />
+        <SearchDialogFooter>
+          <TagsList tag={tag} onTagChange={setTag}>
+            <TagsListItem value="all">All</TagsListItem>
+            <TagsListItem value="core">Core</TagsListItem>
+            <TagsListItem value="cli">CLI</TagsListItem>
+            <TagsListItem value="api">API</TagsListItem>
+          </TagsList>
+        </SearchDialogFooter>
+      </SearchDialogContent>
+    </SearchDialog>
+  );
+}