Hi BlueLily
You sound like such a beautiful deeply caring person. This co-worker is blessed to be working with you, even if they don't entirely know it.
In some cases, it can definitely be hard to know how someone's going to react to others knowing of their mental health struggles. While some may be upset by a number of people knowing, others may be deeply touched by just how much their so-workers/work friends really care. With that 2nd one, this is a factor that can sometimes lead to the development of those friendships beyond the work environment.
If you're unsure of your co-worker's reaction, maybe a 'tread carefully' approach could work. If you've gained a sense of why or how they're suffering, being able to relate to that kind of suffering could be one approach. Openness and honesty can require some degree of vulnerability in some cases. For example, if you're someone who can relate to depression or anxiety or some other mental health challenge, a kind of openness regarding that challenge could be a start. Kind of like starting with 'How are you going?'. If their response is along the lines of 'Oh, yeah, not great' or 'Could be better', this could start a conversation along the lines of 'I tell you what, this place challenges me at times. Sometimes it can act as one of my triggers regarding depression/anxiety/etc'. And then leave it at that but add a knowing and supportive smile, as a sign that you know how impacting certain triggers can be, while it also being a friendly smile of support. Sometimes that can be enough to plant a seed in a person's head, one that grows into a realisation that someone else can maybe relate to their mental health challenges.
If you're a sensitive person, being able to gain a sense of how someone's feeling and acknowledging how they're feeling can be reassuring. If you get a sense that they're stressed, saying 'You look stressed' is acknowledging their feelings. If you get a sense they don't want to be at work or they've had a challenging weekend, saying 'You look like you need a holiday' or 'You like like you've had a tough weekend' could also act as acknowledgement, as well as being something that can maybe open a conversation up. Gaining a sense of how someone else is feeling can indicate to them that we're feeling for them.
I suppose, at the end of the day, all relationships are based on how we relate. If you want to deeply relate to this co-worker as being someone who cares about them, expressing caring ways could be a good start. 'I get a sense that you're upset/stressed and I'm worried about you, as I care about you. It's important you know that'. There can be other ways to relate too, that can make some difference to a person. If they relate to you as 'the person who always leads them to laugh or smile' or 'the person who always feels for them' or 'the only person who points out to them how amazing they are in different ways', there are a lot of different kinds of relationships.
