OP Q: just how much processing would be done on the mining planet before the end result is shipped back to the homeworld?
Presumably all of it; to reduce both the size and mass of the "end result" before shipping. There is no point in shipping slag which is going to be discarded anyway; and for some mining operations (like rare metals and gems) the "end result" is on the order of one millionth the mass of the processed ore. Why ship a hundred thousand tons of garbage rocks to another star system when they contain only a few ounces of the "end result"?
That stuff should never leave the planet surface; all refinement and extraction of the "end result" should occur on the surface. Or in a few rare circumstances, in orbit around the target planet can be more cost effective despite the work of getting the ore up there (or partially processed ore up there); because a zero gravity environment is (theoretically) very useful for certain types of extraction or metallurgy.
Just like Earth corporations, your customers will want the ore in a finished generic form; like sheets, coils, blocks or spools of wire in various gauges. That is what should be shipped from the planet.
The expense of separate factories for doing that, on each planet, might warrant shipping some single form (like easily stackable cubes, or grains (small spheres)) of the pure "end result" to a post-processing plant where those can be formed into customer-desired configurations, or combined into alloys for that purpose.
I am presuming the mining company is not in the business of producing end-consumer products and only producing materials to be melted down (or cut and polished or otherwise processed) by their customer companies.