QWebEngineProfile::setNotificationPresenter() and QWebEngineCookieStore::setCookieFilter() are present in PyQt6 but missing from PySide6. Note they take a std::function (and the former takes an unique_ptr), which might make them difficult to expose.
QWebEngineProfile::setNotificationPresenter(
std::function<void(std::unique_ptr<QWebEngineNotification>)>)
void QWebEngineCookieStore::setCookieFilter(
const std::function<bool (const FilterRequest &)> &filterCallback)