FaceTime on smart TV with screen mirroring

Given that both the Camera and Microphone used for the FaceTime call is present on the iPad, AirPlay to TV makes little (if any) sense. However, you should be able to use Screen Mirroring (from the iPad Control Centre) to mirror your iPad screen to the TV over HDMI or AirPlay connection.

How to AirPlay video and mirror your device's screen - Apple Support

To do this wirelessly you would need to purchase the actual TV box to AirPlay your iPad Pro to the TV box then to your TV.

Can you confirm your iPad model/kind and what iOS version it is, currently, running?