
I fully understand you're frustration and honestly I do agree with you but I think for this case since the boyfriend is an actual nursery teacher which mean he studied everything to know about kids so even if Kota's dad as more experience as an actual father, he's still explained to be a teen parent without a lot of help or actual planning.
I didn't like how many time they bf had to play the intermediate between father and son but at least its justified by his background. And to be fair for a kid (who's extroverted) calling an other man papa isn't that weird.
But if you want some good representation with a guy with kids I would recommend Kiraide Isasete (non toxic omegaverse)

This isn't meant to come off as rude, but their dynamic makes perfect sense imo when you think about it!
I totally get where you're getting at though, because in a lot of childcare manga in general, the "step parent" ends up being more understanding to the child. However, I think in this manga it makes perfect sense and is realistic.
Takeru and his ex had Kota when they were relatively young, and being a young parent on its own is already challenging. When you add the fact that Takeru also a single father who grew up in a household without a model father figure, it makes perfect sense why he's not as skilled at being able to handle Kota in comparison to Aoto. Takeru is also an only child to boot, which means prior to Kota, he had no experience dealing with kids. Meanwhile, Aoto not only grew up with siblings, but is a nursery teacher. Seems like he's been surrounded by children his whole life, making it easier for him to navigate Kota's feelings. I think that's why a lot of times, Aoto seems to know what to say to Kota while Takeru struggles.
So in retrospect, I actually think this dynamic works in context for this particular story! Not to say I don't understand where you're getting at lol! I can see how that can get annoying especially since it's an overused, concept that's typically misused as well.
it always pisses me off when the person dating the parent is better at parenting. when aoto joins the author makes him more understanding and well versed at explaining things to the kid than his actual father. don't even get me started on the whole aoto is more fatherly which is why kota calls him papa for the first time WHEN HE HASN'T EVEN BEEN HERE MORE THAN 5 MINS. very unrealistic kota knows take is his dad. authors always make this happen in childcare bl where the biological father is really bad at understanding his kid and his partner has to show him the right way to parent. it's always "child gets in trouble wrongfully accused and biological father doesn't believe him or scolds him only for his bf to be the only one who understands the child." not saying there aren't fathers that do this, but it's a weird habit I see a lot of manga bl authors doing