> somehow thought any up-to-date iOS device would work. [...] Got the newest iPad?
iOS 12 was the last version of iOS where that name applied to iPad as well as iPhone. Starting with version 13, the version of the operating system for iPhone had been the only one called iOS, with the iPad OS called iPadOS.
So, yes, I suspect that any up to date iOS device does work, through the magic of terminology peculiarities, unless currently supported Apple Watches don't support all currently supported iPhones (I haven't checked if that is the case).
As for the operating system for Apple Watch, that has always been called watchOS.