The Zwift Companion is not currently designed to operate in Landscape mode. Sorry about that.
If you’re not able to download Zwift or the Zwift Companion to your iPad from the App store, typically that means the iPad is too old and not supported for use with Zwift.
If your iPad is not on this list of supported iOS devices, then regrettably it’s not supported:
Requires iOS 9.0 or later. Compatible with iPhone 5s, iPhone 6, iPhone 6 Plus, iPhone 6s, iPhone 6s Plus, iPhone SE, iPhone 7, iPhone 7 Plus, iPhone 8, iPhone 8 Plus, iPhone X, iPad Air, iPad Air Wi-Fi + Cellular, iPad mini 2, iPad mini 2 Wi-Fi + Cellular, iPad Air 2, iPad Air 2 Wi-Fi + Cellular, iPad mini 3, iPad mini 3 Wi-Fi + Cellular, iPad mini 4, iPad mini 4 Wi-Fi + Cellular, 12.9-inch iPad Pro, 12.9-inch iPad Pro Wi-Fi + Cellular, 9.7-inch iPad Pro, 9.7-inch iPad Pro Wi-Fi + Cellular, iPad (5th generation), iPad Wi-Fi + Cellular (5th generation), 12.9-inch iPad Pro (2nd generation), 12.9-inch iPad Pro Wi‑Fi + Cellular (2nd generation), 10.5-inch iPad Pro, 10.5-inch iPad Pro Wi‑Fi + Cellular, and iPod touch (6th generation). Apple TV.
If your iPad appears on that list, then you can also run the Zwift game app itself on the device, and that will appear in the landscape mode you’re looking for.
Any supported iPad will run the game and allow you to monitor your power outputs and other metrics on the iPad screen during your rides.
In theory, using a supported iPad for Zwift will also solve your dilemma where you are craning your neck to see the Apple TV, assuming you’re not able to rearrange your setup and lower the TV screen to a more convenient height.