fix(auth): re-check auth status after logout; clear NextAuth session after sync

1) Sidebar logout flow:
   - After AuthReset, also dispatch AuthStatusCheckSubmitted so the auth
     machine re-verifies storage (not just resets to initialState). This
     makes sure the redirect to /chat reflects the actual storage state,
     not just the forcibly-cleared context.

2) OAuthSessionSync:
   - After dispatching AuthGoogleSyncSubmitted / AuthFacebookSyncSubmitted,
     call signOut({ redirect: false }) to drop the NextAuth session.
     The OAuth idToken / accessToken has already been handed to the
     backend; clearing the browser-side session prevents lingering OAuth
     credential exposure. Fire-and-forget — once status flips to
     "unauthenticated", the useEffect early-returns so no re-entry.

Note: auth-machine.ts lost a 3-line stale comment block about XState v5
type inference for inline assign; bundled with this commit.

src/stores/auth/auth-machine.ts

@@ -32,9 +32,6 @@ export type { AuthEvent } from "./auth-events";
 //   splash / auth screen 看到 `pendingRedirect && loginStatus !== "notLoggedIn"` 跳 /chat
 //   跳完派 `AuthClearPendingRedirect` 置 false
 // checkingAuthStatus 不设 flag —— 被动查 token 不算"用户意图"。
-//
-// 注：onDone 用了内联assign（不是 helper function）—— XState v5 的 TypeScript
-// 推断对 helper return type 不友好；内联能保留 `state.matches("loadingXxx")` 的类型。
 // ============================================================
 export const authMachine = setup({
   types: {