refactor(auth): unify Facebook and Google login into AuthPlatform class

Replace the separate FacebookLogin and GoogleLogin classes with a single
AuthPlatform class that takes a provider name ("facebook" | "google") as a
constructor argument. This consolidates duplicate OAuth sign-in logic behind
one entry point while preserving the existing NextAuth flow.

- Add new src/lib/auth/auth_platform.ts exporting AuthPlatform and
  AuthProvider type
- Update auth-facebook-panel.tsx and splash-button.tsx to use the new API
- Rename initialContext → initialState in the auth machine for consistency
- Update inline docs and comments to reference AuthPlatform

No behavioral change for end users; both providers still route through
NextAuth's signIn() with the same callbacks and cookies.

src/app/auth/components/auth-facebook-panel.tsx

@@ -7,13 +7,13 @@
  * 视觉规格（与 Dart 对齐）：
  *   - Spacer → logo（120h）→ Spacer → Facebook 主按钮 → 链接 → Spacer → 法律
  *   - Facebook 主按钮：46px 白胶囊 + Facebook "f" 图标（#1877f2）+ "Login with Facebook"
- *   - 社交登录走 NextAuth：`new FacebookLogin().signIn()` / `new GoogleLogin().signIn()`
+ *   - 社交登录走 NextAuth：`new AuthPlatform("facebook").signIn()` / `new AuthPlatform("google").signIn()`
  *   - "Other Sign-in Options" 链接打开底部弹层
  *   - 弹层 Email 按钮 → 触发 `onSwitchToEmail`（父级派发 `AuthPanelModeChanged`）
  */
 import { useState } from "react";
 
-import { FacebookLogin, GoogleLogin } from "@/lib/auth/nextauth";
+import { AuthPlatform } from "@/lib/auth/nextauth";
 
 import { AuthErrorMessage } from "./auth-error-message";
 import { AuthLegalText } from "./auth-legal-text";
@@ -33,7 +33,7 @@ export function AuthFacebookPanel({ onSwitchToEmail }: AuthFacebookPanelProps) {
     setBusy("facebook");
     setError(null);
     try {
-      await new FacebookLogin().signIn();
+      await new AuthPlatform("facebook").signIn();
     } catch (e) {
       setError(e instanceof Error ? e.message : "Facebook login failed");
     } finally {
@@ -45,7 +45,7 @@ export function AuthFacebookPanel({ onSwitchToEmail }: AuthFacebookPanelProps) {
     setBusy("google");
     setError(null);
     try {
-      await new GoogleLogin().signIn();
+      await new AuthPlatform("google").signIn();
     } catch (e) {
       setError(e instanceof Error ? e.message : "Google login failed");
     } finally {