Oh I see! That’s looking good. You can use bevel in combination with subdiv, but only in the areas that need sharpening. If you bevel every edge it does become pretty unwieldy. In the bevel modifier, try setting the limit type to Weight. Then go into Edit mode and select only the edges that need creasing and turn up the bevel weight in the sidebar.
To keep things looking sharp, right click in object mode and set shading to Smooth. Keep Mark Sharp and Harden Normals off if using subdiv, but turn them on if not.
