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/app/(home)/blog/page.tsx

@@ -0,0 +1,44 @@
+import Link from 'next/link';
+import type { Metadata } from 'next';
+import { ArrowRight } from 'lucide-react';
+import { blogSource, formatBlogDate, sortBlogPages } from '@/lib/blog';
+
+export const metadata: Metadata = {
+  title: '开发者博客',
+  description: 'cursor-byok 的架构决策、协议实现与开发进展。',
+};
+
+export default function BlogPage() {
+  const posts = sortBlogPages(blogSource.getPages());
+
+  return (
+    <main className="mx-auto w-full max-w-5xl px-6 py-16 sm:py-24">
+      <div className="max-w-2xl">
+        <p className="font-mono text-sm font-medium text-fd-primary">DEVELOPER BLOG</p>
+        <h1 className="mt-4 text-4xl font-bold tracking-tight">开发者博客</h1>
+        <p className="mt-4 text-lg leading-8 text-fd-muted-foreground">
+          记录 cursor-byok 的架构决策、协议实现和开发进展。
+        </p>
+      </div>
+
+      <div className="mt-12 divide-y border-y">
+        {posts.map((post) => (
+          <Link
+            key={post.url}
+            href={post.url}
+            className="group grid gap-3 py-7 transition-colors hover:text-fd-primary sm:grid-cols-[10rem_1fr_auto] sm:items-center"
+          >
+            <time className="text-sm text-fd-muted-foreground">{formatBlogDate(post.path)}</time>
+            <div>
+              <h2 className="font-semibold">{post.data.title}</h2>
+              <p className="mt-1 text-sm leading-6 text-fd-muted-foreground">
+                {post.data.description}
+              </p>
+            </div>
+            <ArrowRight className="hidden size-4 transition-transform group-hover:translate-x-1 sm:block" />
+          </Link>
+        ))}
+      </div>
+    </main>
+  );
+}