The recently released new Apple TV app is not available for Sony TV, they have their own Apple TV app which need Sony to release firmware update to support the Apple's DRM.

You can sideload the new app & login but can't play the content. It will give DRM error..

Only some Sony TV 2017 & newer model that has received firmware update in 2021 but didn't receive the Apple TV able to use the new Apple TV app by sideload.

Here's how to differentiate the apps:-
Apple TV - Google TV & Android TV
Package name: com.apple.atve.androidtv.appletv

Apple TV - Sony TV(Google TV & Android TV)
Package name: com.apple.atve.sony.appletv

That's expected. Sony need to update the TV with newer fimware first that has the required DRM for Apple TV app..

Maybe can try to watch on TV web browser.
Iinm, Sony TV comes with pre-installed web browser on their Android TV or you can try JioPagesTV browser which is built for Android TV with EME(Widevine) support..

Someone did test the latest app & doesn't work..
The only way to have the app working is by updating the TV firmware..

The Bravia Core has nothing to do with Apple TV app. It is a separate service provided by Sony Pictures.
Also, the service is only available on new Bravia XR model & not available for Malaysia.
Refer: https://www.sonypicturescore.com/faq/EN/us