Automated Solution to Match Categories Across Different Sites which have Diff Category Names

We looking for options or solutions to solve manually time consuming task that we have. We own numerous sites but category mapping is set to be different due to websites different target markets. Also some sites have different API etc so we must map to their cat mapping instead of our own. The solution we looking is below: Is to create solution that pulls all the categories from all our sites weekly to have update categories. Then has funcitonality for us to link them. Example would be on Site A we might have Bedroom>Beds>Single but on Site B we might have Home&Garden>Bedroom>Beds>Single etc. So what we want to do is somehow tell it if we upload new product file it return cat mapping to all sites. So we only need to map products for our largest site and it returns cat mapping to use on other sites. We also have issue where by we api from one supplier with 1k cat and 40K products and we want to add another api with 20k and it's own category. Ideally we would come up with solution that would auto assign cats from 20k supplier to change match into 40k supplier. So every new product from smaller suppplier will auto map into relvant cat from other supplier. Otherwise we end up 2 caterogies that have similar products and too many dupes. Open to all solutions bar manual options!