For the benefit of all, as you have evidentially discovered, by far the easiest method to trigger and save a screenshot is to set-up and use the corner-swipe gesture. This feature, that can be triggered with either a finger or Pencil gestures, can enabled or disabled from iPad settings…
- Open the Settings app on your iPad
- Go to the General menu and then choose the Gestures option
- Make sure “Allow Finger to Swipe From Corner” is enabled
- Choose the action you want (Screenshot) when swiping from either (or both) the left and right corners - or disable by selecting OFF
With the corner swipe enabled, you can easily capture a screenshot with just your finger (or Apple Pencil). Just swipe diagonally from the lower-left or lower-right corner of the screen towards the centre; this will immediately trigger the screenshot.
The other ways to trigger a screenshot from an iPad are described here:
Take a screenshot on your iPad - Apple Support