Using parent/guardian is appropriate when you don’t know the family situation, I think.
I work in primary and use the term “a grown up at home” if I don’t know the kid well- some kids live with aunties, grandparents, are in care etc. Some don’t have mums due to bereavement, some have been left by parents. So there’s all that as well.
Obviously you wouldn’t say “your grown up” to a uni student, but if you don’t know who they have at home it is genuinely inclusive to use parent/carer. I would say if you know your student lives with mum/etc it’s better to use the word mum/etc.