I had trouble at first finding how to force the relevant software update. My Sony Bravia (model KD65A1, purchased March 2018)is a Google one and last year I could not even install the Apple TV app. It wasn't offered in the Google store. Then in January this year I discovered it was now available and so installed it to be able to watch Bad Sisters. When it was unwatchable I, I searched for help and stumbled upon this thread, and by switching to SD only was at least able to watch the series with minimal picture problems.
I thought my TV was set to automatic software updates, so when I checked last week to see if problems had been resolved by an update (as other writers had found) and discovered they weren't, I was puzzled.
Instructions on how to locate software update controls did not apply to my TV model so went exploring and finally found the answer. Might help others.
Go to Home Screen
Go to Apps
Go to Help
Go to System Software Update
Select System Update - "check for update and install"
As soon as this was done I checked Apple TV and everything was perfect in HD - finally!
Looks like the issue might have stemmed from Apple/Google compatibility issues perhaps. And in future I will check for software updates manually rather than assuming Sony will supply them automatically.