If you still use one of the older Apple TV boxes without tvOS and the App Store, you will no longer be able to watch Netflix as of July 31, 2024. AirPlay is not supported either.
In addition to 2014 Sony TVs, Netflix is also ending support for the 2nd and 3rd generation Apple TV boxes that were launched in 2010 and 2012, respectively, according to MacRumors.

The 2nd and 3rd generation Apple TV boxes have a different remote control. Photo: Apple
These Apple TV boxes do not run Apple's tvOS like the newer generations. The old boxes also no longer receive software updates from Apple, making it difficult for Netflix to "maintain the best possible Netflix experience", according to an email sent to customers.
The Netflix app will remain available on Apple TV HD (4th generation) and all generations of Apple TV 4K.
AirPlay not supported either
A fallback option on the 2nd and 3rd generation Apple TV has always been to use AirPlay via an iPhone or iPad. Almost all streaming services today support AirPlay.
However, Netflix made the decision in 2019 to remove AirPlay support from its app, after Apple made the decision to implement AirPlay in TV models from various brands.
Instead, you should consider upgrading to Apple TV 4K (review). There are also cheaper options such as FireTV, Roku and Chromecast with Google TV, but they are increasingly turning into ad billboards for not just streaming content but also general items like food and cars.
- Source: MacRumors