Switch from Node.js + pnpm to Bun runtime and package manager

Replace @libsql/client with bun:sqlite for zero-dependency SQLite access,
swap drizzle-orm/libsql adapter for drizzle-orm/bun-sqlite, and rewrite
Dockerfile to use oven/bun:1-alpine. The raw Database instance is no longer
exported via Proxy (native C++ methods lose `this` binding through
Reflect.get); instead, a closeDatabase() helper handles graceful shutdown
and the health check uses Drizzle's db.run() directly.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/api/health/route.ts

@@ -1,9 +1,10 @@
+import { sql } from "drizzle-orm";
 import { NextResponse } from "next/server";
-import { client } from "@/lib/db/client";
+import { db } from "@/lib/db/client";
 
 export async function GET() {
   try {
-    await client.execute("SELECT 1");
+    db.run(sql`SELECT 1`);
 
     return NextResponse.json({ status: "healthy" }, { status: 200 });
   } catch {