New install from iCloud complete, no cannot get out of Settings

Try a forced-restart of your iPad:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

Noting that iPadOS 15.3 is current, have you actually performed the forced-restart as suggested?

You are very welcome.