Do you know that he is unhappy, OP? Or are you extrapolating from an idea of what would make you unhappy?
Because the young person you are describing could have been my Sixth Form self. Though as this was before the invention of screens, I spent all my time reading instead. I was not depressed in any way, I was getting on with my life, but I was quite introvert and needed the downtime after the time at school. In me that was not a sign of depression.
Otoh when my dd holed up in her room and stopped socialising, that was a sign of depression- because she's not me and what is healthy for me is not healthy for her.
So what I think is useful in this situation is to have a general look at his wellbeing:
does he appear very negative in his general outlook? (often a sign of depression)
does he seem to be "letting himself go" in terms of not eating properly, not washing etc
is there anything he seems to enjoy, even if it's online? (not getting any pleasure out of life is a sign of depression)
do you think he is managing his studies? (this is something you'll have to be gentle about, as the university, very rightly, will not be discussing it with you)