Speaking from personal experience, that person is very likely depressed AF. The bubbly person you see at work is her putting on a brave face to get through the day without making things worse by putting people off in showing her real self. The “jokes” are a subconscious attempt to see if anyone actually cares enough about her as a person to pick up on the hints she’s dropping. If you approach her about it directly, tho, she’ll put up a wall because she doesn’t know your true intent - do you actually care, or are you gonna make her life worse by doing something like trying to have her committed?

If you truly care enough to get involved, and try to help her then doing it well is going to require some commitment to subtle and supportive interactions. You can try to privately let her know that you’ve picked up on the hints, that you get it, and that she can come to you for support if and when she’s comfortable with doing so. You likely will have to give her space and time to figure out if she can really trust you while also occasionally (i.e. don’t push it or otherwise overdo it - let her be in control) reminding her that you care and were serious about the offer of support.

If that’s more than you’re up for, then maybe just let her know you’ve noticed so she doesn’t feel completely ignored, and offer to help her find mental health options to deal with her depression.

At least this is what I’d want as somebody who has lived through several decades of inadequately treated depression. I, too, am a sincere, straightforward person who likes to help, and find living in a world full of people who routinely aren’t so honest (even or especially with themselves) extremely depressing and difficult to deal with.