How do I add the apps on a second Apple TV?

Keep apps and the Home screen up to date across multiple Apple TVs

If you have more than one Apple TV associated with the same iCloud account, you can keep the same appearance and apps for each device. This makes it seamless to switch between an Apple TV in the bedroom and one in the living room, for example. 

1. Open Settings  on Apple TV.
2. Go to Users and Accounts > iCloud and turn on One Home Screen.

Customize the Apple TV Home screen - Apple Support

Or You can go to the App Store - purchases to see your apps to download

It can be automatic, if both models are 4th generation or later, and when you have set One Home Screen.

Customize the Apple TV Home screen - Apple Support

• Keep apps and the Home screen up to date across multiple Apple TVs