[RedNote] 扫码和 Cookie 都成功后, check_login_status 仍可能误判为未登录

The problem description is as follows: I am using a RedNote overseas account. After adding the `rednote.com` backend to the local branch, the scanning and cookie persistence have been successful, but the `check_login_status` still returned "not logged in". Further inspection revealed the following: - The modification time of the cookie file is updated after the scanning is confirmed; - There are `web_session` and `id_token` under `.rednote.com` (the cookie domain has not been modified); - Calling the `search_feeds` function with the same session can return the actual results; - Therefore, at least in this case, the scanning and the session itself are valid, and the problem is concentrated in the login status detection. Related background: #609, #699. #812 has already explained that RedNote should use `/login` to obtain the QR code; this issue mainly supplements the false negative problem of `check_login_status`.