Is he oblivious to Killua's emotions? Or does he simply not care?
Well 🤓☝️ let's talk about it!
Gon loves Killua a bunch, that is something we know because he says so. He's his first friend, the way Gon is Killua's first, and he's important enough to make Gon want to spend the rest of his life with him.
1) He says Killua's the only one for him (volleyball match)
2) that he's fun to be around (stargazing on whale island)
3) he is more confident and is able to be more selfish with him out of trust (volleyball match)
4) he's able to calm down when Killua touches him, like water to a flame (jajanken against morel)
5) he listens to Killua as much as possible, even while lost in vengeful anger (not killing Pitou instantly and choosing to wait, believing Killua's judgment despite his own thoughts on the matter)
Just a few little instances where we're shown how important Killua is to Gon, and how he proves so by his words and actions. He definitely loves him, and while I do think it's a pure love not yet categorized into romance— does that mean he's dense to what Killua feels?
Whether it is romantic or strictly platonic, Killua's feelings for his best friend run incredibly deep. It's a profound kind of love that makes him selfless and loyal, a kind of love that makes him willing to die alongside him— it's something that's difficult to process, let alone speak of. We spend a lot of time in his head, enough to figure out that Killua has to resort to metaphors and idioms to describe those feelings.
And he's willing to go down in flames with that light, as lovers.
And we're always led to believe that everyone can see the extent of those feelings but Gon himself— while we're shown that Gon's usually the first to notice the littlest details.
The first time we really see that well is in the volleyball match. After the first throw, Gon looks surprised when Killua holds the ball again and gets ready for a second punch. Gon is well aware that Killua's hurt, and wasn't planning to go for a second time due to the fact— until he saw the determination from his best friend who'd mentioned that he had nothing to be determined for months prior. It's unspoken, and even Killua hadn't noticed that Gon knew about his hands until he had voiced it out loud.
Gon is perceptive, and a lot more emotionally intelligent than we give him credit for— just not necessarily adept at processing some difficult emotions with maturity and grace. Still, he's able to tell and understand a lot about other people, especially his best friend.
Another time we see him notice something about Killua but not voice it immediately was right after the date with Palm. Killua carried him out, and he noticed a difference in demeanor and the small injury on his forehead, which he later brings up. Though in that case, Killua was more dismissive.
So with Gon having noticed those little details that Killua was making some efforts to hide, we can tell that he's not blind to subtle changes. And with how he'd gone along with him and opted to not bring it up instantly, we can tell that he's aware of Killua's more secretive nature when it comes to his feelings— it wouldn't be far fetched to say that Gon was able to tell that there are things Killua can't talk about, emotions he simply can't afford to share. It makes sense that Gon wants to give him that space, because he's not one to force discomfort onto loved ones (at least not intentionally).
So, is he dense and oblivious?
If anything, he's the opposite! Killua just puts effort into hiding and avoiding certain topics, and Gon simply respects him and doesn't want to pry into uncomfortable territory. He's waiting for when it's necessary, when he's asked, or when he just thinks is the right time to bring certain things up— which could either be never or whenever Killua himself is ready.
After all, he must be pretty aware of Killua's more cold exterior, being the one who carried a lot of the emotional load at the beginning of the series (befriending and comforting Canary and Gotoh in Killua's place, being a more active voice of kindness with Zushi, and accepting Bisky's help for the both of them when Killua was still hesitant)
So you can say that while Killua is there to protect and care for Gon (mostly) physically, Gon is the one caring for Killua emotionally. He just can't do it perfectly when the boy is so secretive, and he himself is still a preteen who went through something he wasn't equipped with handling at all. In a way, the CAA also highlighted Killua's codependence on the emotional regulation Gon has (at least when he's not being a bit too selfish), and put Killua on the spot with his own underdeveloped sense of emotions.
Ughhh they're so silly....