I would caulk all around the window opening, sealing the stucco to the window. Don't caulk the black window weep hole.
Generally if the house had proper rainscreen behind the stucco it wouldn't matter. Stucco is a water sink so it will absorb water. Any water that gets behind the stucco should have a drainage plane to get out. Generally you'd osb/plywood your framing, then you apply building paper/tyvek/typar/etc, then you apply 1/2" or thicker vertical strips or a stucco drainage mat. You then chicken wire or stucco on top, leaving an air gap behind for drying potential. Older construction didn't use a rainscreen and instead relied on the wall cavities being empty and drafty to allow drying potential.
Is there a metal window header flashing with side dams on the exterior above the top window trim?