Connecting wireless keyboard to Apple TV.

See here: Use Bluetooth accessories with your Apple TV - Apple Support

Apple TV (3rd generation) supports one bluetooth device, and that is a keyboard.

Apple TV (3rd generation) Technical Specifications - Apple Support

The process of pairing the keyboard with your Apple TV:

1. Put the keyboard in pairing mode. Many Bluetooth keyboards have a dedicated Pairing button that you press (or hold) until a light flashes to indicate pairing mode. Others (including Apple’s Wireless Keyboard) require you to press and hold the keyboard’s power button until the pairing-mode light flashes.
2. Use your Apple TV’s regular remote to navigate to Settings﹥General﹥Bluetooth. The Apple TV will automatically begin searching for nearby Bluetooth devices that are in pairing mode.
3. Once your keyboard appears in the list, select it and press the Select key on the Apple TV remote.
4. After a few seconds, you’ll be prompted to type, on the keyboard, a four-digit code that appears on your TV’s screen. Type that code and press Return or Enter, and you’ll receive a confirmation message that the keyboard is now paired with the Apple TV.

Apple TV will remember this paired device, until you tell it to forget the device.

If the LED is blinking, then it is in pairing mode. If the LED burns continuously, then it is paired to another device. You may need to unpair the keyboard from a previous host, before you can pair to a new device.

Set up your Apple wireless mouse, keyboard, and trackpad - Apple Support

I can’t say if these newer models wireless keyboards have compatibility issues for older Apple TVs. But the specs say that the 2015 model and 2017 model wireless keyboards require newer macOS software with Macs. So I’m not hopeful on that front.