A member of staff who has MS is under no obligation to inform their employer of the fact, so unless the colleague they DID tell was an “official channel”, so to speak (e.g. HR), then technically, you have heard what you should not, and I’m not sure the person who told you was within their rights to do so, though doubtless they had the best of intentions.
Without knowing more about the context, it’s difficult to say. But an employee who hasn’t chosen to approach you, despite being advised to (whether officially, or unofficially, I don’t know) presumably doesn’t want/need any adjustments at the moment?
It’s not automatic that having MS always means adjustments are needed. People can sometimes be OK for months or even years, so if they are managing fine, they may choose not to do or say anything that draws attention to their diagnosis - ironically, for fear of discrimination. So, whilst you and the colleague who told you may think it would help and protect the employee, they may fear such “help and protection” would itself be discriminatory - e.g. that you might “shelter” them from promotion, for fear it could prove too much - whether or not they’d expressed any such reservations themselves.
I do think you’ve been placed in an unfortunate position. If it’s HR that has told you, I do think that counts as “official”, and you should seek their advice about how to play it.
But if it was a mutual colleague, then, unless the employee comes to you themselves, it’s really no more than office tittle-tattle. Has the intermediary breached a confidence by telling you? If it was something said privately to a friend, then presumably, the employee would not have expected it to be repeated straight to you?
I agree you now have to tread carefully, because you cannot unknow what you know, regardless whether you were supposed to hear it or not. So you have to be mindful of your legal obligations. But equally, you cannot foist adjustments on someone who has not requested any, and may not even have wished to disclose their illness.
Of course, now, you are always going to be looking for signs they’re ill or struggling, which might have been exactly what they were hoping to avoid! I really think you’re going to have to leave the ball in their court on this one. I don’t really see how you can go to them, and say: “I’ve heard you might have MS, is this true?” Their health status is private, unless they choose to share it, so even asking the question could be viewed as intrusive and irrelevant.
Being pragmatic about it, how likely is it the employee would bring a claim over failure to make adjustments for a condition they’d never told you about? Unless they told the third party with the full intention it should “get back”, or it became a sort of open secret that everybody knew, why would they be expecting you to do anything about it? It doesn’t seem very logical that somebody would choose NOT to approach you about any needs, but then complain they weren’t met! The law doesn’t require employers to be psychic.