As of 2023, Instagram does not notify users when someone takes a screenshot of their posts or stories. However, there have been instances in the past where Instagram has tested this feature on a small number of users. In 2018, Instagram tested a feature that would notify users when someone took a screenshot of their story, but the feature was not implemented for all users.
It is worth noting that Instagram does have a feature that notifies users when someone takes a screenshot of a disappearing photo or video sent through Instagram Direct. If you send a disappearing photo or video to someone through Instagram Direct, the app will notify you if the recipient takes a screenshot of the message.
In summary, Instagram currently does not notify users when someone takes a screenshot of their posts or stories. However, the app has tested this feature in the past and may implement it in the future.