The only "official" way to use Fitness+ on a TV is with an AppleTV HD or AppleTV 4K box. AirPlay does NOT work at all. Lightning to HDMI cables do not work either. There has been some success with a USB-C to HDMI cable for modern iPad Pro devices working but its unclear if that is something Apple will break too when they realize its an option.
Believe me, I'm not happy about it but I spent $179 (minus a $50 gift card on black friday from apple) on a new AppleTV 4K just for my fitness room TV but it works SEAMLESSLY with the whole family who have Apple Watches and Fitness+ is great with it, in terms of a "fitness equipment" expense and an investment in my health it isn't so bad, but as a 3 year old streaming box the price was absurd.