Watch movie on TV

Sony have only introduced airplay for particular models (2018 and newer), the same would be true for the app. In order to cast or use the app you can look for an external streaming device. You can check the link for the full list of compatible devices.

Apple TV app - Devices - Apple (CA)

there are Chromecast apps in the app store if the tv support that

also maybe search for sony to see if they have some apps which can do something like it over wifi.

I am not familiar with that retailer unfortunately, but the main options would be Roku, and Fire TV if you want casting (airplay) and the Apple TV app. There are more options if you just want the app. Check the link above to see the full list and then check if that retailer offers any of those devices in store.

The OP was specifically referring to airplay and the Apple TV app.

You're welcome