Apple TV 3rd Generation

That is incorrect. Those are preset channels that are sent via server and based on basic web templates. The 4th gen and 4K have app stores with apps that are developed for and run on a completely different system (TVOS). The hardware cannot support the OS nor does it have space for apps. The last update for the 3rd gen was over a year ago, and apart from a rare addition from Amazon to the channels list it has seen no other support.

The 3rd Gen doesn't have apps and as it's discontinued it no longer is updated. You can continue to use airplay with apps that support it, but developers can also choose to block it

The 3d generations DOES have apps, just not downloadable ones, and Apple could easily add Hulu Live TV via a software update (that the 3d generation devices still get).