Given that he is involved with her as her employer, I think he deserves to understand the situation. If Nanny has expressed a desire to keep the information private, ask her for permission to share it with him, or ask her to explain to him.

36 is awfully young to have arthritis
Of course you should tell him about the arthritis. How do you even question that?

Doesn’t seem particularly confidential to me tbh 🤷‍♂️