Unable to exit iPad recovery mode

First try leaving recovery mode with a force restart. Unplug the iPad from the computer, then:

iPad without a Home button: press and quickly release the volume button closest to the top button, press and quickly release the other volume button, then hold the top button until the Apple logo appears.

iPad with a Home button: hold the Home and top buttons together until the Apple logo appears.

If it starts up normally, you are done. If it goes straight back to the recovery screen (cable pointing at a computer), the system software is damaged and a button trick will not fix it. Connect it to a computer (Finder on a Mac, or the Apple Devices app on Windows), and when you get the choice, pick Update first. Update reinstalls iPadOS without erasing your data.

If Update fails or it loops back to recovery again afterwards, the remaining option is Restore, which does erase the iPad, then you set it up from your iCloud or computer backup. Use a known good cable and a different USB port if the computer does not see it, and if you get a numbered error during Update or Restore, post the number here, it points at the cause. If it still will not come out of recovery after a full Restore, that is usually hardware and it needs Apple service.