Trying to use Notability in split-screen mode on iPad
drag it to the right half of my screen
It could be that you’re not letting go of the app far enough to the right — try dragging it to the right edge of your screen.
with one app open
It could also be that this app you have open doesn’t support being in split screen. Try with Safari as the first app.
If an app is in slide over mode, how do I get it into split-screen mode?
Drag the small pill-shaped handle at the top of the slide over app slightly towards the left/right edge of the screen. The app behind will move out the way for you to let go in the space.