Apple Box and Youtube tv

The Apple TV (3rd generation) (A1427, A1469; 2012–2016) does not support user-installed apps.

The Apple TV 4K (3rd generation) (A2738, A2843; 2022–) does support user-installed app.

The YouTube TV app for Apple TV requires system software version tvOS 12 or later, according to Google’s App Store submission. The old model Apple TV (3rd generation) maxes out at system software version 7.9.

No, you can't download apps to the Apple TV (third gen). You are limited to what is pushed to the device. I believe YouTube discontinued support for that model a while back.