Niall, great reflective essay on importance of team sports. I agree with all your points about not just team sports but any sport.
I would go one step further and stress the importance of a team sport and an individual sport. As you age out of the junior level and want it just for recreational purposes, it would be difficult to pull together a soccer or basketball pick-up game. With the individual sport like tennis or golf it becomes easier to organize and engage.
It's never too late to start, you know? You don't have to aim very high. Treat it for what it is which is for recreation and a chance for physical, mental, and emotional well-being.
Have you tried a sport like pickleball which is getting very popular? It needs some eyehand coordination but no real coaching needed to the likes of a game like tennis which is very technical. How about ping-pong or table tennis?
Never too late! As Trevor Noah said, it's not worth living in regret. "Failure is an answer, rejection is an answer. Regret is an eternal question you will never have the answer to."