[Not_here]

This is a problem that has been going on for me as well. And you articulated what the problem is really well. Especially on weekends, I have more time to kinda pull myself through and no one would know what it took for me to get my homework done because I survived anyway.

Personally, I am not keen in telling a supervisor or teacher because it's almost as if their position distances me from them and it's a professional setting, not a personal one. It makes me sad sometimes that the people around me don't care much, and that there's so much they may never know about me, but then again our interactions are more about exchanging functions.

What I would do is, confide in friends. The teacher might not even notice especially if they're university professors and have hundreds of students. But a supervisor might because they work with smaller groups. So either family/friends and perhaps a supervisor or teacher if they make themselves approachable.

I just don't know how understanding they'd be. They'd still want work done. And you might not want to feel like you get off the hook due to your anxiety/depression because it's a helpless feeling. Personally I like to feel i'm getting things through despite my mental health. But at the same time I'd want someone to know "just in case" Just not to be treated differently. To not treat me as "disabled" or "disadvantaged".

It's definitely a complicated issue. I don't have a definite answer. I guess you might want to ask yourself "What are you looking for to happen after you tell them?" Do you want them to just know. Do you want them to do something about it like accommodations. Do you want them to become a supportive figure.
Also, is it important that it is a supervisor or teacher that you tell? Will you be satisfied to talking to a friend or counselor or is it important that the boss of your internship etc is the one who is aware.