Netflix has chosen to not support AirPlay anymore since 2019. Use the Netflix app on your smart TV or Apple TV box instead.
The screen you are seeing is known as “Conference Room Display”. It has an on|off switch in Settings﹥AirPlay. To get out of this screen, use the Menu button on your Apple TV Remote.
This setting could theoretically be locked with a PIN code through Restrictions, or maybe even through a device profile (if set up that way, usually through corporate MDM). I assume you know the origins of your devices.
If you lost the remote for your Apple TV - Apple Support
- You can buy a replacement remote from Apple.
- You can use the software remote on your iPhone, if both devices are already connected to the same home network.