As described, you appear to be swiping downwards from within the visible area of the screen - which will expose Spotlight Search and associated Siri Suggestions.
Swipe downwards from the very top-right corner of the screen - starting from the bezel edge, beyond the visible area of the screen.
If you continue to experience difficulties, perform a forced restart of the iPad:
Force restart iPad (models with Face ID or with Touch ID in the top button)
If your iPad doesn’t have the Home button, do the following:
- Press and quickly release the volume button nearest to the top button.
- Press and quickly release the volume button farthest from the top button.
- Press and hold the top button.
- When the Apple logo appears, release the top button.

Force restart iPad (models with the Home button)
Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
