Idk while Fury could've learned more I thought it seemed like he acknowledged he was in over his head when he asked Gi'ah for help. I do think SI had a poor ending
Acknowledging you're in over your head isn't growing. Especially not when it's followed up by him running right back to space with the only difference between the start of the show and the end being that this time he took his wife with him.
Kate learning that her instincts aren't perfect also isn't really growing, but it's basically on the same level of 'learning' the Fury did. With the major difference between them being that Kate isn't the only major character in the show and her story doesn't require her to grow and learn a lot. The show still works perfectly fine in terms of characterization despite her limited growth. Whereas Fury is far and away the star of the show and his story (and with it the entire show) doesn't really make a whole lot of sense in large part because of his complete lack of character arc.
And Kate and Clint caused collateral damage during their fights. I don't recall her learning anything from having her mom arrested. She reacted like Clint's crimes were nothing. She just fangirled him the whole time.
Every Superhero ever has caused collateral damage during fights. The Avengers once contributed to the wholesale destruction of an entire country. It's pretty much foundational to the genre. What matters for the characters is that they try to prevent people from getting hurt and to limit the possible damage where they can and they don't irresponsibly start superhero fights in crowded civilian areas. This show meets that standard just as well as the vast majority of the genre, and better than plenty of individual examples (including examples that I - and most people, as far as I can tell - would consider better shows/movies overall, like the Guardians of the Galaxy for instance).
As for her reactions: Your constant repetition that she 'didn't learn anything from her mom's arrest' is nonsense. She learned that her mom was a villain and that the guy she thought was evil was actually the good guy which means that she learned her instincts aren't perfect and fighting evil is messy.
Is that incredibly basic and generic? Yes. Does it significantly change who she is? No. Because the whole point of her story from the beginning is that she already has the heart of a hero and she's not going to let the world hold her back from being true to that. That's what her story is about. Overcoming the world holding her back from what she knows she wants to be (her mother included). Her story is not about her learning to be a better person, no matter how much you want to judge it on that yardstick.
Also, she didn't completely freak out about Clint's past because she was exercising compassion and helping Clint overcome his demons. That's also a thing that superheros very often do, even for people who had far worse pasts than Clint.
Whereas Fury didn't just accept whatever people told him and vice versa.
Fury's entire story is about uncovering an evil skrull conspiracy. Of course nearly every single episode of it involves him verbally sparring with the bad guys. That's what spy thrillers *do*. That still doesn't change the fact that all of that back and forth is horribly written and completely unconvincing with the only real exception in the entire show being the scene between Fury and Rhodey - which is entirely undermined by the revelation that Rhodey isn't really Rhodey so everything he said in that scene is pure bs to play mind games on Fury.
Also, Kate absolutely did not just accept whatever people told her. If she had, there would've been no story at all because she'd never have tried to become a superhero at all.
I struggle to see anything interesting about Kate. Even Kamala did the fangirl thing better by not being a selfish brat
If I'm being honest here, it sounds like what you struggle with is the ability to maintain any sort of objectivity whatsoever towards Kate because you just hate her personality.