Where is the rotation lock button

Just swipe straight down from the very top right corner, and it should work every time. There's around 3 fingers worth of area at the very top of the screen next to the corner where it works. It should not be difficult to find the spot at all.

It works for literally millions of people, as otherwise, there would be countless posts about it here no doubt, which there aren't.

In control center as shown in the support document you posted from.

It's the one with a lock and an arrow around it, just below the Wi-Fi icon.