Use more geometry. With curved surfaces you, sadly, will have to have a resolution on your cylinders that roughly matches the size of your bevels:
Maybe some sub-d-magicians here have some better solution, but that is my takaway from my limited experience.
Edit: I just realized a deeper source of this issue. You want to create a transition between a cylindrical shape and a shape with a rectangular cross section. Alternatively, you may consider replicating the cylinder’s curvature onto the hinge itself. This, however, is a design choice.
(blender version 3.4.1)
cylinder_cylinder_tansition_3.4.1_v01.blend (938.9 KB)