Now in landscape orientation, note that the labels for the kind of capture (cinematic, video, photo, etc.) do not rotate, but all the camera icons do: 0.5, 1.5x, and 2, and the icons and text at ...

Ensure your iPad isn't locked in portrait orientation to avoid the Sidecar app rotation bug. Once SideCar is all set up, you then need to install BetterDisplay on your Mac and create a virtual screen.

If turning on and off the Rotation Lock won't let your iPad screen shift from portrait to landscape as you'd like, first try closing all the apps you're using — that may alleviate the issue.