How do I download the app icon to my TV so it appears like all other apps at the bottom of my screen when the TV turns on?

UTU8000

You appear to have a 2020 model Samsung TV from the UHD 8 series. Those models are listed as supporting the Apple TV app. List of Apple TV app-supported smart TVs and third party streaming devices - Apple. If your question is for a different model TV, then check the list, or specify the model number here.

Then the Apple TV app is either pre-installed, or downloadable from Samsung’s App Store.

Use apps on your Samsung smart TV - Samsung Support

↳ Install and use apps on the TV

• Apple TV app user guide for smart TVs and other devices - Apple Support
• Watch in the Apple TV app on Samsung smart TVs - Apple Support