On Sony TVs, the Apple TV app is currently not supporting in-app transactions. That means that the buy or rent transaction will have to be done on a different supported device (e.g. iPhone*). Once the transaction is completed the content will be available in the Apple TV app on Sony TV as well, as the purchase is linked through the Apple ID account. The “How to Watch” blurb was supposed to convey that.
Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support
[footnote] 2. In the US, you can subscribe to Apple TV+ on Amazon Fire TV, but you can't purchase other content from the Apple TV app. On Amazon Fire TV (in other regions), Android TV, and Sony TV devices, you can't purchase content from the Apple TV app. You can buy, rent, or subscribe on another supported device and then watch in the Apple TV app on your Amazon Fire TV, Android TV, or Sony TV device.
*Devices that you may use for the in-app transactions for the Apple TV app are: iPhone, iPad, iPod touch, Mac, Windows PC, Roku, Roku TV, Xbox, PlayStation, LG TV, Samsung TV, Vizio TV, VIDAA TV.