I don't have any apps on my home screen (which consists of medium calendar, weather, and Siri suggestions widgets) and new downloads are set only to go to App Library.
I've recently downloaded a couple of apps that I decided fairly quickly decided I no longer wanted. When I went to look for them in 'Recently Added', they were not there. I could find them in the full list (pulling down while in App Library) and the only way I could delete them was to long-press the app from within the App Library list, have it show up on the Home Screen, and then delete it after a long-press to get the option to do so. I would expect the app to be in 'Recently Added' and that I could delete from there without the extra steps. It's only happened a couple of times so I haven't determined yet how long it takes for new apps to show up in 'Recently Added'.
I've recently downloaded a couple of apps that I decided fairly quickly decided I no longer wanted. When I went to look for them in 'Recently Added', they were not there. I could find them in the full list (pulling down while in App Library) and the only way I could delete them was to long-press the app from within the App Library list, have it show up on the Home Screen, and then delete it after a long-press to get the option to do so. I would expect the app to be in 'Recently Added' and that I could delete from there without the extra steps. It's only happened a couple of times so I haven't determined yet how long it takes for new apps to show up in 'Recently Added'.