WhatsApp does not send typing notifications when you are simply reading previous messages in a chat. Typing notifications are triggered when you start typing a new message or responding to a message in real-time. So, if you're only reading old messages and not actively typing a new one, the other person won't receive any typing notification.
However, please note that app features and functionalities may change over time, so it's always a good idea to check the latest version of WhatsApp and its settings to see if there have been any updates or modifications related to typing notifications.