Long story short, I took Haru to a vet today and after some testing stuff found out he has a form of kennel cough (we're waiting on the lab results to know which virus/bacteria is the root cause).
Fortunately it never got to a very serious point. Just enough that I was kinda concerned and as a first-time puppy parent decided I wanted to be safe rather than sorry and bring him in.
From the tests they did have results for, it seems like some mild pneumonia/inflammation was present in the upper respiratory system.
So now he's on antibiotics and won't be able to play with other dogs for 3 weeks.