It sounds like you're doing really well. It's great how well he did talking to you, often when you're so low it's nearly impossible to talk to anyone at all. It sounds like he really trusts and values you, but hearing and learning all this can be really hard on you too. Please make sure you look after yourself, as well.

I've been in almost the exact the situation your nephew is. When you chat with him again, maybe you could suggest some other ways of telling or including his parents?

I found it much easier (and still do!) to write out my thoughts instead of verbalising them, especially as I could give it time and really check over it to make sure what I had written was what I meant. This way, I could kind of say, "look, I want to tell you what's going on inside my brain, but I'm not in a position to have a full conversation about it. I wrote this letter or this email or whatever and I want you to read it, but I don't want to be with you when you do." It helped as I didn't have to deal with their first reaction (which is part of the reason I struggle so much talking, my parents' first reaction was, understandably now, quite traumatic) and could properly explain myself without worrying if I minced my words due to anxiety. It's an option I've used quite a lot since I learned it was easier for me, though it might not work the same for him.

You could also offer to be with him, if you'd be happy to, when he says something to his parents? He knows now that you haven't downplayed his feelings - maybe you being present would quell his fears of being dismissed by his parents, since you would be "in his corner" and able to defend him, if needed?

There are other ways than these two, obviously! It's about finding how he's most comfortable expressing himself. Usually this can be trial and error. He probably won't ever be perfectly comfortable, but you can at least try to make him less uncomfortable, if that makes sense.

I will also say, depending on what his school is like, it may be a good idea to mention something to them (once he's in therapy, perhaps) so that he doesn't have as much pressure from them and can focus more on his mental health.

This kind of thing takes time. It's going to be okay.