Console isn't appearing in library within the app.

Hello, first it's a pleasure to be able to help you today.

My name is welcome to the community.

Hello Matthew, when you say "isn't appearing in library" is referring to your game library that should appear on the console, or you tried to connect console via streaming on PC and it does not appear.

You say you set up the console via App, which App would be and most importantly, have your Microsoft account added and logged into the console?

If you can give more details, I'll be waiting for your reply.

depends, was it for pc or the xbox console, if pc then download via the library in the windows store or xbox app. if console then download from within the library on the console.

If the game isn't hidden, as the above poster mentioned, it's possible that perhaps you've ticked some of the filters within My Games and Apps which is why some of your games aren't showing up. When you're in the My Games and Apps section, and in your Full
Library, scroll over to "Filter" and double check that you're looking at "All Console Types".

It's most likely to be a game you've hidden by accident (or somebody else hid by accident) though.

Have you tried checking on the status of App Installer within your Microsoft Store library?

The My Games or Library would be within the Microsoft Store app on your PC while signed in with your Microsoft account.