I think Apple support is confused. The only words out of our mouths when talking to them should be "AirPlay". We want to use an officially supported device - iPhone, iPad, Apple TV (device!!) that is able to run the current generation operating systems. THEN - we want to use an external monitor for display. We would like to talk to that external monitor with AirPlay. (I'd even accept a cable solution if they can make that work reliably, but that is not what this thread is about.)
The external monitor just has to support AirPlay - it doesn't need a single app on it - no Netflix, no Apple TV (app), no imagined Fitness+ app, etc etc etc. The whole topic of a smart TV with apps is confusing the issue.
Now, modern Roku devices support AirPlay (
I think). So you can consider such a Roku with its attached TV to be a single thing - an external monitor that you connect to with AirPlay. Such a Roku could have no apps on it at all. It's just supporting Airplay to get the picture to the TV. The particular apps running on the Rodu is confusing the issue the same way the apps on the smart TV is.
When Apple says you can't use your TV with AirPay because the TV is not a supported device - challenge that. You can use headphones when using Fitness+. That's an external audio device in the same fashion that we want an external video device.
I think the people who have had luck with Apple have found a support person who understands the simple thing being requested.