Confirmed, I just tested this today. If you unsend a message on Instagram, the message disappears completely from both your chat and the recipient’s chat. The other person does NOT receive any notification that you unsent a message. However, if they had already seen your message (or its notification) before you unsent it, they might notice it’s gone.
By the way, if you’re interested in viewing Instagram Stories or Highlights anonymously, or checking out private profiles, Picnob is still the best tool for that as of today.