feat(docs): add documentation site and demo features

- Introduced a new documentation site for Cursor BYOK using Next.js and Fumadocs.
- Added a product demo page with a corresponding Vite configuration.
- Implemented a demo API to simulate LLM calls and responses.
- Enhanced the Makefile to include new build and development commands for the documentation.
- Updated package.json scripts for building and running the documentation site.
- Created various components and layouts for the documentation structure, including blog and user documentation sections.
- Added styling for the new components and layouts to ensure a cohesive design.
- Included a README and other necessary files for local development and deployment.

apps/docs/proxy.ts

@@ -0,0 +1,32 @@
+import { NextRequest, NextResponse } from 'next/server';
+import { isMarkdownPreferred, rewritePath } from 'fumadocs-core/negotiation';
+import { docsContentRoute, docsRoute } from '@/lib/shared';
+
+const { rewrite: rewriteDocs } = rewritePath(
+  `${docsRoute}{/*path}`,
+  `${docsContentRoute}{/*path}/content.md`,
+);
+const { rewrite: rewriteSuffix } = rewritePath(
+  `${docsRoute}{/*path}.md`,
+  `${docsContentRoute}{/*path}/content.md`,
+);
+
+export default function proxy(request: NextRequest) {
+  const result = rewriteSuffix(request.nextUrl.pathname);
+  if (result) {
+    return NextResponse.rewrite(new URL(result, request.nextUrl));
+  }
+
+  if (isMarkdownPreferred(request)) {
+    const result = rewriteDocs(request.nextUrl.pathname);
+
+    if (result) {
+      return NextResponse.rewrite(new URL(result, request.nextUrl), {
+        // this URL has two representations, selected by `Accept`
+        headers: { Vary: 'Accept' },
+      });
+    }
+  }
+
+  return NextResponse.next();
+}