The App Store is not on my Apple TV gen 3

The Apple TV App Store became available with the 4th generation model. It is not available for earlier models. Paramount+ says to support Apple TV (4th generation or later). Peacock TV says to support Apple TV (4th generation or later).

Supported devices - Paramount+ Help Center

How can I stream Paramount+ on my Apple TV? - Paramount+ Help Center

↳ Supported models and versions

What devices and platforms are supported by Peacock? - Peacock TV Help Center

Paramount+ app - App Store preview - Apple

↳ Information﹥Compatibility﹥Apple TV﹥Requires tvOS 13.0 or later

Peacock TV app - App Store preview - Apple

↳ Information﹥Compatibility﹥Apple TV﹥Requires tvOS 13.0 or later

IF you want additional content you need to upgrade to an Apple TV HD or 4K model. I would recommend the 4K model. You can find them on Apple's store or Amazon or a variety of other resellers. In short, your Apple TV 3 simply does not have the ability to add the App Store which is necessary to add additional apps. Please do yourself a favor and upgrade to the 4K model, it is a HUGE upgrade.