How can I watch Apple TV on my Sony TV?

If the Apple TV app is available for your smart TV, then you should be able to download it from the on-device App Store. For Android TV models, that would be the Google Play Store: HOME﹥Apps﹥Google Play Store. Then search for “Apple TV”.

If the Apple TV is not listed as available for your model TV, then that means that your model TV isn’t supported (at this time).

Unsupported models TV can use an external streaming device.

All the ways to watch in the Apple TV app - Apple Support

Watch on your TV

Apple TV box (4K, HD, and 3rd generation) ﹥

Streaming devices ﹥

Smart TVs ﹥

Gaming consoles ﹥

List of Apple TV app-supported smart TVs and third party streaming devices - Apple

List of AirPlay 2-enabled smart TVs - Apple

if your tv is not on the list

Apple TV app - Devices - Apple

then you need to purchase an appletv box and connect it to the tv's hdmi port

Once Apple released the app to the manufacturer it is up to them as to which of their models are supported. You don't necessarily have to get the Apple box if you don't want to spend that, it would also be available on Roku, FireTV, and Google TV.