Search terms from paid campaigns are the fastest source of honest keyword research you will get. They show the exact phrasing that converts, including modifiers your category pages never mention, which turns into collection copy, filter names and new landing pages.
Running in the other direction, strong organic coverage lets paid budget concentrate. When a category ranks well, you can pull back on the head term and put the money into products or queries where you have no organic presence, which usually improves blended efficiency without losing volume.
The practical sequencing for most stores: use ads to establish which products and offers deserve investment, while SEO work goes into the categories those tests validate. Report the two together on blended cost per new customer rather than in separate meetings, since the same shopper often meets both before ordering, and a channel that looks expensive alone can look sensible in the mix.