Yes, visual effects and animations in UIs burn cycles just to make it look nicer. Doesn't matter if it's a website or the native system UI.

To be clear, I'm not saying it's fine to constantly render when you know nothing changed. I'm saying the load from this should be very small. Most of the performance issues from this page are actually from the header animation, which you can delete in the inspector to see a significant drop in usage (mine went from ~35 to ~6.6 CPU).