It’s both. It was co-developed by the companies.

No, the actual hardware wasn't. That's the point of the entire exercise to not develop the product in-house. Microsoft only develops Windows game mode. https://www.8bitdo.com/ultimate-3-mode-controller-xbox/ is not a Microsoft product (or "co-developed with Microsoft) either. It's yet another 3rd party product with Xbox branding and why would Microsoft have a say on the price then?