It did not work. It use to do it all the time, all of a sudden it won’t do it any more.

Take a screenshot on your iPhone

1. Press the side button and the volume up button at the same time.
2. Quickly release both buttons.
3. After you take a screenshot, a thumbnail temporarily appears in the lower-left corner of your screen. Tap the thumbnail to open it or swipe left to dismiss it.

Take a screenshot on your iPhone - Apple Support

For Screen Recording check your Screen Time Restrictions.