I think this is well in the realms of normal. We all have different ways of dealing with intense stress.
You are kind to be worried about your friend, but I don’t think four weeks is that long to not hear from someone, especially if they have a lot going on.
I know a lot of people unburden themselves by talking through their problems , and reaching out for emotional support, however, not everyone finds this helpful. Personally, I instinctively disappear into myself. I’m naturally introverted, anyway, and even in normal circumstances I need quite a lot of time to recharge. However, if I am having a tough time, I find it completely overwhelming, having to keep up with even the most mundane social stuff. I’m also a private person, and I don’t find opening up to other people about my problems helpful.
I do try to let people know that I’m taking some time out because things are difficult, but sometimes I find even that, anxiety inducing (also I worry that I might come across as thinking I am so important, everyone is going to notice me being offline/not answering my phone for a week😟).
The one exception, is I have an old school friend, who I am v close to. We basically, grew up together, and we talk about absolutely everything. We have the same outlook on life, and there is no judgement.
So, your friend who is having a hard time, is it possible she is just closer to your mutual friend than you realized? Or, maybe it was just down to timing(ie, a work phone call came when they were together?)? Or, is it possible she has been in a similar situation herself, so she is has useful advice she can give.
I don’t think there was anything wrong with the reply Mutual Friend gave you - it sounds like she passed on the message, but she was wary saying anything more on the situation, as it is not her story to tell.