Function connectivity_check_handler 

pub async fn connectivity_check_handler<Api: Send + Sync + 'static>(
    __arg0: State<UiState<Api>>,
    jar: CookieJar,
) -> Html<String>

Handler that checks internet connectivity by attempting TCP connections to well-known anycast IPs and returns an HTML fragment. Manually checks auth cookie to avoid UserAuth extractor’s redirect, which would cause htmx to swap the entire login page into the widget.