First of all, the search bar at top of the start menu is a good idea imo, but now, its closes the start menu and opens the search tab. Start menu closes, new search window opens, they do not have the same size, there is always a closing and reopening effect going on. I think thats not a good user experience.
I wanted to share some opinions:
It would be better if the that transition happens without closing the start menu and reopening the search menu. Some quick resizing animation like expansion shrinking would make that transition better imo.
Second one is the functionality of the search bar at top of the start menu. Currently it does not have a filtering or searching in quick start apps or on all applications context. It would be wonderful if the search bar filters the the applications in the all applications or quick start apps menu, rather than opening the search window from scratch.