Written by Mark Gurman Apple Inc is ramping up work on a mixed-reality headset, its first major new product category since the Apple Watch, and has renamed the accompanying software in the latest sign of an approaching debut. The company plans to introduce the headset as early as next year, along with a dedicated operating system and app store for third-party software, according to people with knowledge of the matter. Internally, the company recently changed the name of the operating system to “xrOS” from “realityOS,” said the people, who asked not to be identified because the project is still under…