Having read the bulk of the thread and caught up a little on the context of the relationship, there are a lot of ways you could see this charitably if you wanted to. It certainly comes off as stiff, awkward, frankly odd. It’s possible she’s just not the type of person who “clicks” with you and didn’t feel comfortable with a more open, compassionate response to your bereavement. It’s also possible she was REALLY up tightly trying to open a little door for you to talk to her/lean on her if you wanted. Her upbringing might have been incredibly formal or like many people in my family encouraged more exuberant displays of affection towards people not in the family (sounds weird, but you can have a stiff upper lip attitude within a family while trying to keep your friends sweet).
With a different eye, she’s doing less than the bare minimum and to be honest it IS a bit weird. Examples from me - two (strangely unknown to each other) friends were bereaved by the suicide of the same person this year. I started with the formal phrases: I’m sorry, that’s so awful, etc but based on what I know about what my friends believe and the details they’d given about this person there was much more I could say, always acknowledging I couldn’t take away the pain of loss, because nobody can. I don’t think I helped much, although they both said I did, but it’s always better to try and fail than to try to protect yourself from awkwardness by not trying.
This may come out as unintentionally harsh, but I think the important takeaway from this situation is that you’ve lost two precious people, not that someone with whom you have a distant and formal relationship has responded badly. Focus on the people around you, share with them, lean on them for a while, remember your relatives and have compassion for yourself. It’s not doing anyone any good to reserve headspace for anger/upset about someone not responding correctly to the bereavement, particularly since it sounds like it’s within the pattern of her normal behaviour. Maybe even consider that she wasn’t being outright cruel, just very distant, and it’s not worth the time and energy to even want to get much closer.