I think you're correct. I have the Gen1 4K TV as well and no FaceTime app.
Also - https://www.macrumors.com/2023/06/05/facetime-launching-on-apple-tv-with-iphone-and-ipad-camera-integration/#:~:text=The%20feature%20requires%20a%20second,for%20camera%20and%20microphone%20functionality.
Upgrading to Beta 2 did not cause it to appear, so I think that's that.
Armyflier
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