Hi Max @Max-Erl
A fast alternative is, to select the Camera and then the Plane and then:

It will also move the Camera to the Plane, so you have to correct that. You could, for instance SHIFT+S > Cursor to selected before the alignment. And afterwards, SHIFT+S > Selection to Cursor (both with only the Camera selected of course).
Or just move the Camera by hand.
You’ll also probably have to Rotate the Camera 90° one one or more of it’s Local Axes.