I how do I search for an app on my iPad?

Use Search on your iPhone, iPad, or iPod touch - Apple Support

From the iPad's Home screen, take your finger put it at approximately smack dab in the middle of the iPad’s screen, away from any icons, and swipe downward with that finger.

This will bring down the iPad's search box feature.

Works for me every single time.

As the article states:

”Swipe down from the middle of the Home screen.”

You are likely starting your swipe too high on the screen.