Is it real stucco, or is it EIFS (Exterior Insulation and Finish Systems)? https://www.buildingscience.com/docu...-and-solutions

With stucco, it is hard as concrete. With EIFS, it looks the same, but if you push your thumb into the wall with a lot of force, the wall flexes a bit, or is soft to the touch.

I see cracks like that all the time, but since that does not fall under what I can address for my job, I don't have any input on what you need to do to fix it. I'm interested in what you find out!