Thanks!
I’ll fill in what I found out so anyone else with this problem can save time.
I phoned and was told that I would need to purchase a new Gen4 Apple TV in order to get classes to visually show on the screen.
Apple programmed Fitness+ so the app will not allow airplay fitness+ video on a Gen3 Apple TV. The music plays but it will not mirror video for this specific app from my iPhone. And I can’t upload the new update to the TV which would upload the Fitness+ app directly on there either, as Apple don’t send this software update to the older Gen3 units.
Essentially the new iPhone, new Apple Watch, current Fitness+ subscription and Apple TV are not enough to make this work - I have to also purchase a new TV Unit.
I can airdrop many other fitness classes through third party subscriptions (Fiit, Peloton) so I’ll stick with those.