Kittens also need a good amount of fats in their diet, hence nutrient-dense kitten foods have more fat than adult food. I'm talking about kibble here. Forget the supermarket or cheap brands, feed a really good quality brand and your kitten will feel fuller for longer. They will poo less and it won't smell as much. Poor quality food has a heap of fillers and also less desirable quality of meat used in manufacture.
To be honest, a kitten that is old enough to eat dry food doesn't need to be fed wet food. It's kind of like McDonald's to them, unless it's a super high quality food. Even then, they don't need it if they are fed a good quality dry. Having said that, I still feed my guys a small amount of wet food once a day at dinner time. They don't "need" it, but they like it.
I have two kittens who have just turned one and I also have an older cat (had two older cats until last week 🥺). I have always 'free fed' dry food, i.e. it's always available. I have only had one cat (current old cat) who is unable to self-regulate and is therefore fat. However, the vet said he's healthy despite his weight, so I'm not concerned. The kittens have fed themselves from 8 and 11 weeks of age, when I first got them - they are rescues born three weeks apart and raised in the same foster home so they behave like brothers.
The elder kitten is absolutely obsessed with any kind of food - cat or human food. I've never seen anything like it in all my years of owning cats (and I've had quite a few). Every time there is food around, he gets exactly the same look on his face as he does when he's hunting 'prey' outside (like a lizard or something). He will then stalk the food, as though I can't see him. It's truly bizarre! I've had plenty of cats try to beg for human food, but never one try to actively hunt it!
It's just who he is as a kitten/young cat. Not something I've seen before, but cats never stop surprising me. He's just a very active social kitten and he's grown into a delightful young cat - who still tries to hunt everything food related. Your kitten will be fine. ☺️