
What needs to be changed to make it look like in the second picture?

What needs to be changed to make it look like in the second picture?
As mentioned by the others before in the comments, the second image is in Object Mode - The beveled edges will not show in Edit Mode. What you need to change in Object Mode to make it look like that: Either enable Geometry > Wireframe in the Overlays for the viewport (which would show the wireframe on all objects) or in the Object Properties under Viewport Display enable Show > Wireframe, which would only make it visible on that object. By the way, using these methods the modified wireframe would also be visible in Edit Mode, but it is not selectable and will be shown together with the original mesh, which can be distractive for editing.