Apple TV app "Video not available" message on Sony Bravia and Roku 3810x

I have a Sony Bravia KD-43X80J smart TV and a Roku Stick 3810x plugged into another TV. The Sony and Roku are both on the list of Apple TV App–Supported Devices at https://www.apple.com/apple-tv-app/devices/.

I have the Apple TV app on both the Sony and the Roku. On both, I can log in, go through the menu, and select a show or movie. But every time I hit PLAY, I get the message "Video Not Available. There's a problem loading this video. If this continues, check your internet connection."

Here's where it get strange: I have no trouble streaming Apple TV content to my MacBook Pro or iPhone 8 on the same Wi-Fi network. It's only the non-Apple devices that are giving me trouble.

Other details: Fast internet service (100 MB). ARRIS CM820A cable modem. TP-Link AC4000 wireless router.

All other streaming services work fine on both the Sony and the Roku. I've done all the usual stuff - reinstalled apps, power cycled devices, etc.

Any ideas? Apple Support told me to call Sony and Roku, but it seems absurd that I'd have the exact same error on two different devices. It's getting maddening.