Why is the notifications toggle missing on Libby app on iPad?

Delete the Libby App from your iPad - then perform a forced restart of your iPad before reinstalling the Libby App from the App Store:

Delete apps on your iPhone or iPad - Apple Support

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:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. 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.

Go to settings… notifications… scroll down to the app… you should be able to set it there.

Deleting and reinstalling the App will ensure that your App has the most recent version installed.

Delete the app and reinstall it. During this process the app should ask you if you want notifications turned on…

It could more the app not the update. Contact the developer.