I'm not sure what legacy platform you're referring to
You're writing a Mac app in Objective-C. If you encounter problems with that combination, you're usually going to have to figure out a solution yourself. There aren't many other people doing that.
OK, it appears that the new role property of NSSegmentedControl is what changes the appearance under macOS 27. Apple should make clear that the style property is ineffective.
Documentation isn't Apple's priority. There's 25 years of legacy UI documentation and behaviour that is going to be different depending on 1) the Xcode SDK you're using, 2) your minimum deployment version, and 3) the OS version your app is running on.
You can see this very clearly in NSSegmentedControl's documentation. There's lot's of it, isn't there? But it's not complete. Certain properties, methods, and enums don't seem to have any. If you click on them, you'll see why. Anything that was introducted in 10.13 or later isn't documented. That's 9 years now that Apple's stopped updating the documentation.
For modern systems, the expectation is that you'll use SwiftUI. I'm not saying you should do that. I tried it for a new app and gave up after six months. Never finished the app either.
You can still use the legacy languages, targets, and platforms, but it will be your responsibility to understand how they work and test them on all supported OS versions. Sometimes you can use virtual machines anything before 26. But 26+ adds so much GPU-heavy UI that you really need real hardware for testing.
These APIs and behaviours on different OS versions can and will change, even with minor versions. As I said before, the best way to insulate yourself is to write your own code. If you don't like the new behavout of NSSegmentedControl, you'll have to re-implement it. It wouldn't be difficult. It's a simple control.