The translated emails cover what was asked for in this topic. One related gap remains on the push side and is written up separately: Content localization: push notifications for new posts are sent before the translation is stored
In short: the push notification for a new post is queued when the post is created and looks up the translation before it has been stored (about 2 seconds later on the site measured), so it carries the original text. With #44240 the email for the same post is translated, and the two will differ.