Apple Fitness+ and Apple TV 4K

I am using Fitness+ on my iPad but the picture is too small for me. I don't have an Apple watch.

I read that Apple TV will work with any TV that has an HDMI input. This is what I have; it is not AirPlay enabled and is not one of the Apple Smart TVs.

I'd like to know for sure if I can just use the Apple TV to access my Fitness subscription content. I'm reluctant to buy the Apple TV 4k if I can't basically see all my content on my TV as though it were an enlarged iPad screen.

I don't want to buy a watch and, apart from the set-up I don't want to have to fiddle around with the iPad every time I use it.

Grateful for some clarification - thanks