Thank you. I read your initial post, and the entire thread before replying.
You seem to looking for features on Apple TV that don't exist, the Password/security and Verification code areas.
Please read this from the link I posted. These are the login steps.
- enter Apple ID
- enter password and stop
- use Settings on your phone to request a code, see this link: Get a verification code and sign in with two-factor authentication - Apple Support halfway down
- add the code to your password and send it.
The instructions to get the code from your trusted device are the following"
Get a code from Settings on your trusted device
If you can’t receive a verification code on your trusted devices automatically, you can get one from Settings, even if your device is offline.
From your iPhone, iPad, or iPod touch:
In iOS 10.3 or later:
- Go to Settings > [your name].
- Tap Password & Security > Get Verification Code.
In iOS 10.2 or earlier:
- Go to Settings > iCloud.
- Tap your Apple ID username.
- If your device is offline, tap Get Verification Code. If your device is online, tap Password & Security > Get Verification Code.
From your Mac:
- Go to Apple Menu > System Preferences > iCloud.
- Click Account Details.
- If your device is offline, click Get Verification Code. If your device is online, click Password & Security > Get Verification Code.
So, you see, the "Password & Security" and "Get Verification Code" steps are on your trusted device, not on Apple TV, which just presents a dumb login, same as always.
I hope that's clearer now.