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/stores/auth/machine/auth-context.tsx

@@ -0,0 +1,86 @@
+"use client";
+/**
+ * AuthContext：基于 XState v5 的 React Context Provider
+ *
+ * 业务事件（`Auth*Submitted`）通过 `useMachine(authMachine).send()` 派发。
+ * XState 自动处理异步副作用（invoke + fromPromise actors）。
+ *
+ * 兼容性：保持原 `useAuthState()` / `useAuthDispatch()` API，
+ * 内部将 XState 状态机快照映射回原 `AuthState` 形状。
+ */
+import {
+  type Dispatch,
+  type ReactNode,
+  createContext,
+  useContext,
+  useMemo,
+} from "react";
+import { useMachine } from "@xstate/react";
+
+import { authMachine } from "./auth-machine";
+import type { AuthEvent, AuthState as MachineContext } from "./auth-machine";
+
+/**
+ * 对外暴露的 State 形状（保持与原 AuthState 兼容）
+ */
+interface AuthState {
+  authPanelMode: MachineContext["authPanelMode"];
+  authMode: MachineContext["authMode"];
+  email: string;
+  password: string;
+  username: string;
+  confirmPassword: string;
+  isLoading: boolean;
+  errorMessage: string | null;
+  isSuccess: boolean;
+  loginType: MachineContext["loginType"];
+}
+
+const AuthStateCtx = createContext<AuthState | null>(null);
+const AuthDispatchCtx = createContext<Dispatch<AuthEvent> | null>(null);
+
+export interface AuthProviderProps {
+  children: ReactNode;
+}
+
+export function AuthProvider({ children }: AuthProviderProps) {
+  const [state, send] = useMachine(authMachine);
+
+  // 映射 XState 状态机快照 → 原 AuthState 形状
+  const authState = useMemo<AuthState>(
+    () => ({
+      authPanelMode: state.context.authPanelMode,
+      authMode: state.context.authMode,
+      email: state.context.email,
+      password: state.context.password,
+      username: state.context.username,
+      confirmPassword: state.context.confirmPassword,
+      // isLoading 仅来自邮箱登录 actor（社交登录改由 NextAuth 处理，UI 自行管 busy 状态）
+      isLoading: state.matches("loadingEmailLogin") ||
+        state.matches("loadingEmailRegister"),
+      errorMessage: state.context.errorMessage,
+      isSuccess: state.matches("success"),
+      loginType: state.context.loginType,
+    }),
+    [state],
+  );
+
+  return (
+    <AuthStateCtx.Provider value={authState}>
+      <AuthDispatchCtx.Provider value={send}>{children}</AuthDispatchCtx.Provider>
+    </AuthStateCtx.Provider>
+  );
+}
+
+export function useAuthState(): AuthState {
+  const ctx = useContext(AuthStateCtx);
+  if (!ctx) throw new Error("useAuthState must be used inside <AuthProvider>");
+  return ctx;
+}
+
+export function useAuthDispatch(): Dispatch<AuthEvent> {
+  const ctx = useContext(AuthDispatchCtx);
+  if (!ctx)
+    throw new Error("useAuthDispatch must be used inside <AuthProvider>");
+  return ctx;
+}