My apps do not show up on my Sony Apple TV.

only the appletv box has apps like ipads and iphones

tv's which support appletv app just have access to appletv+ and movies , tv show rentals

not all tvs support the appletv app read Apple TV app - Devices - Apple

if you want to know more All the ways to watch Apple TV+ - Apple Support

you install the apps using appletv app store

Download apps on your Apple TV - Apple Support

not all apps you may have on your ipad or iphone are available in an appletv version