Why was the Junkers Ju 87 not upgraded with a jet engine?
First, the Ju-87 was not easily shot down. It had manoeuvrability superior  to all fighters due to its lower wing loading and Junkers flaps, and it could take a lot of damage. With the rear-facing observer the Ju-87 pilot was in a much better position to evade all maneuvers of a pursuer. Only when faced with large numbers of enemy fighters could a Ju-87 not escape.



Battle damage on a Ju-87 (picture source)

But to put a jet engine into an airplane with a fixed landing gear will not make it faster than the much sleeker piston-powered designs to its days. Instead, the idea was to develop a new design with a retractable gear and a prone pilot position. This was the Henschel Hs-132, pictured below (source)