Does design actually affect conversion?
Clarity does; style barely. Two stores with completely different looks convert similarly if both show the price, the delivery date and the return terms without hunting.
What decides it
Where design earns its money is trust and speed — a page that looks maintained and loads quickly. Redesigns that change the look without changing what is visible reliably produce no measurable difference.
The part that gets skipped
Consistency beats cleverness. A customer learns your store once, and every screen that behaves differently costs them.
The photograph is usually the product page. Everything else is supporting it.
Most design decisions on a store are really navigation decisions, and navigation is what decides whether somebody finds the thing they came for.
Where an app fits
The same screen designed several ways is the point: a catalogue of four hundred lines needs a different home screen from one of forty.