refactor(auth): switch to class-based social login and v4 route handler

Migrate from function-based social login helpers (`facebookLogin`, `googleLogin`)
to class-based services (`new FacebookLogin().signIn()`, `new GoogleLogin().signIn()`),
updating call sites in `AuthFacebookPanel` and `SplashButton` with try/catch error
handling. The NextAuth route handler is also refactored to the v4 pattern, importing
pre-built `GET` / `POST` exports from `@/lib/auth/nextauth` instead of constructing
the handler inline with `NextAuth(authOptions)`.

src/lib/auth/auth_gate.ts

@@ -0,0 +1,28 @@
+"use client";
+/**
+ * 客户端鉴权门（class-oriented 封装）
+ *
+ * `useState` 是 static 方法而非实例方法（hooks 必须在 React 函数组件中调用，
+ * static 方法本质上仍由组件调用，hook 链合法）。调用方写法：
+ *
+ * ```tsx
+ * function MyComponent() {
+ *   const { isAuthed } = AuthGate.useState();
+ * }
+ * ```
+ *
+ * 原始 Dart: nextauth-helpers.useAuthGate()
+ */
+import { useSession } from "next-auth/react";
+
+export interface AuthGateState {
+  isAuthed: boolean;
+}
+
+export class AuthGate {
+  /** 必须在 React 函数组件内调用（useSession 是 hook） */
+  static useState(): AuthGateState {
+    const { data: session } = useSession();
+    return { isAuthed: Boolean(session?.user) };
+  }
+}