Make the source unambiguous
For a silhouette, remove specks, close gaps, and simplify fine lettering before tracing. A PNG to STL workflow cannot reliably guess whether a faint shadow is part of the object. Inspect the outline at the size you plan to print: tiny islands in the image can become disconnected pieces in the mesh.
SOURCE CHECK
For a two-level plaque, aim for one clear foreground region and one clear background.