fix: harden auto-login selectors and poll auth status

app/main.py

@@ -33,6 +33,12 @@ def auth_guard(request: Request):
     require_bearer(request, settings.api_keys)
 
 
+async def _is_logged_in() -> bool:
+    assert lingma is not None
+    st = await lingma.auth_status()
+    return bool(st and st.get("id"))
+
+
 @app.on_event("startup")
 async def on_startup():
     global lingma, auto_login
@@ -52,6 +58,8 @@ async def on_startup():
         headless=settings.auto_login_headless,
         timeout_sec=settings.auto_login_timeout,
         max_retry=settings.auto_login_max_retry,
+        verify_logged_in=_is_logged_in,
+        verify_timeout_sec=max(30, min(180, settings.auto_login_timeout)),
     )