On one hand I’m not entirely sure that the changes in Windows 8.1 for the Search contract and app sizing count as a “new API”–but they are certainly things you need to pay attention to!
Variable app sizing is certainly a new feature for Windows users, and thus something that apps want to handle well. This is one case where some APIs (like tryUnsnap) are actually deprecated! For apps written in HTML/CSS/JS, this means that the view state media features of (fullscreen-landscape, snapped, filled, and fullscreen-portrait) are obsoleted, replaced by the CSS3 standards for responsive web design, namely the orientation feature (portrait or landscape) and using max-width and min-width. I demonstrate some of this in Chapter 2 of my second edition preview. I’ll have more in my Layout chapter in the next preview, but you can also see more in the //build talk Beautiful Apps at Any Size on Any Screen (2-150).
Search also changes in that the Search charm now reaches out to web content, not just in-app content. As a result, in-app search is a feature that an app should show in its own UI (on-canvas or app bar). See Design and Build a Great Search Experience in Your App (3-144) for the details.