Migrate middleware.ts to proxy.ts for Next.js 16 and fix build errors

Next.js 16 renamed middleware to proxy. Merged session-based auth and
API key auth into a single proxy.ts. Also fixed: auth route handler
exports, missing card component, Button asChild type errors, signIn
return type, Drizzle eq() type narrowing, and useSearchParams suspense
boundary.

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

src/app/api/auth/[...nextauth]/route.ts

@@ -1 +1,2 @@
-export { GET, POST } from "@/auth";
+import { handlers } from "@/auth";
+export const { GET, POST } = handlers;