First off, I do think URLs help theme pages, which can indirectly help with SEO, but that shouldn't be your main goal. Aim to create a consistent structure for how all category, subcat, product detail pages are organized. This will not only make your life a whole lot easier, but it will also make more sense to users, help keep linking consistent, and (indirectly) help rankings.
I would have 3 category pages that lists all relevant products: /gallery-wood, /prefinished-wood, /parquet-reclaimed-wood. I would probably then have subcategory pages that drill-down to more specific product listings (i.e. /gallery-wood/brown-engineered-flooring). *This is the page level you'll want to target "brown engineered flooring."
From there, you have to decide if you want the product detail page URL to follow the folder structure (i.e. /gallery-wood/brown-engineered-flooring/[product-name]) or if you want it to only have the product name (.com/[brand-product-name/number]) which is usually better for complex ecommerce sites where products fall under multiple categories.
You could also drop the parent category from the URL structure, which is probably what I'd do. Something like:
- Category: /gallery-wood *optimize for "gallery wood" & related terms
- Subcategory: /brown-engineered-flooring *optimize for "brown engineered flooring" & related terms
- Product Detail: /brown-engineered-flooring/brand-product-name *optimize for brand, product name & related terms
Depending on search volume, there may even be an opportunity to create brand categories or landing pages.
I hope this helps!