Categories decide what shoppers can find. A product in the wrong one - or in none - is invisible in your navigation, no matter how good the photo is.
Fixing that today means opening products one at a time, or using a bulk tool that applies to the entire catalogue at once. Neither is what you want when you are reorganising a shop.
This app lists every product with the categories it is currently in. Narrow the list to what you care about: products in no category, products in a particular category, products NOT in one, or just search by name. Tick the ones you want.
Then pick an operation. Add to a category, and everything the product already belongs to is kept. Remove it from one category and leave the rest alone. Move it so it sits in a single category. Or clear it out entirely.
Before anything is written you get a preview: each selected product with its current categories and what they will become, plus a count of the ones that would not change at all.
Works with both catalog versions. Nothing is saved until you press apply.