I just checked Spotify, and it seems like yes, it does now get focused automatically, not sure if it was always that way, or I just feel that I need to click the textbox after choosing the menu item on the left hand side.

That being said, it was still much friendlier to have a search box that you could click on straight away. From a UX perspective, you need to move your focus away from where you have clicked, because the textbox is in a different area of view.

Clicking back on the search menu clears the search that you were doing. It's fine, you can click the back button, but the old Spotify client (iirc!) would keep your previous search in the search box.