You are right, although I'd caveat it as a *mostly* first person. Nyx has us look into thoughts, moments, or scenes, that the MC wouldn't know about.It's a first-person narrative. You see almost nothing that isn't from the MC's perspective (hedging, in case I forgot about a random scene or two where he isn't present...) so it's unlikely that he would see Melissa cutting anyone's hair, unless it was Emily perhaps, or someone else close to him.
You do get to 'hear' thoughts some of the people are having, such as the dilemma Lexi has with herself when she finds out who MC is in the early chapters, for example. Even getting glimpses into Mel's dreams if she fantasizes about the MC. But the use cases seem to be more purpose driven to tell the stories.
There are also a few scenes where the MC isn't present, but we still get to see. Most obvious being the more contentious retelling of Emily's date with John to Mel. MC wasn't there yet, but gets to hear the retelling. Same with at the end of the update with the Ethan/Zach conversation. Also what happened inside the bar as part of John's plan and audible with Erynn. But again, most of them are for driving the plot and stories forward. It'd be much more interesting than jsut seeing the MC sit in the car for 10-15 screens worth of time while John is inside.