Food Network and HGTV for 3rd gen Apple TV

The 3rd gen only had preset content sent via server, and providers are starting to drop support. If they offer an IOS app that supports airplay then you can use that to stream. As above, you would need a current model to gain access to the app store and download further content.

only 4g and 4k models support apps

the 2g and 3g models only support apple server channels and if food network is not listed as apple server channels only way to get them is to get apple to add more channels to their servers