She started off as an interesting character with traumatic childhood(hardly interesting considering it's Berserk)
As the neglected daughter of a wealthy noble family living in the religious capital of the Holy See, Farnese's childhood is very unique within Berserk, so reducing it to "traumatic childhood, hardly interesting" feels like trolling, or at the very least a thoughtless statement. Not to mention that her backstory is actually much more nuanced than that and revolves around her codependent relationship with Serpico.
then in millenium falcon, she loses most of her complexity. She waters down and is just a caretaker for casca which seemingly solves all her issues and trauma without any coherent transmission set early on in Millenium Falcon arc.
This makes you sound like you haven't actually read the manga. If anything, her character becomes more complex in the Millennium Falcon arc, and that directly follows her development throughout the Condemnation arc. Her fragile worldview, which she had constructed to protect herself as a result of her childhood, is completely shattered by the supernatural events she witnesses. That's why she seeks Guts out.
Caring for Casca, which she has to do if she wants to tag along, is difficult for her at first. We see her progressively better herself and find comfort in the fact she has to protect someone else. It forces her to be stronger and affirms her true personality instead of the false posture she had fabricated in order to appear strong to others. This in turn leads her to realize that to truly overcome her fears, she has to understand the world. And to do that, she decides to learn magic. It's a masterclass in character development.
Taking care of Casca helped her overcome her issues, but it really shouldn't have. Imagine if she had to slowly, painfully deconstruct her childhood trauma, and put herself back together. Imagine Serpico having to choose whether or not to keep passively encouraging her dark sides. Imagine if she didn't just find a metric ton of kindness buried in her, but instead had to pry that kindness out of herself inch by inch.
If Berserk was a story focused on Farnese's emotional journey, you could have had 41 volumes of her going to the therapist and examining her feelings. But Berserk is Guts' story, and while Farnese's development occurred, so did his, as well as Isidro's, Serpico's, Schierke's... not to mention the Kushan invasion and Griffith's campaign against them. We were introduced to magic, to new key characters, Guts faced off against Slan, obtained the berserk's armor, and so on.
So yeah, you only get to see certain key moments of Farnese's development. That's why it's good storytelling: because those moments are dense and nuanced enough to form a cohesive whole that captures her journey, even though there's only a few of them. What you describe is wrong, too. Farnese is shown being incompetent, cowardly, and impatient with Casca (going so far as to yell at her). She lacks confidence, and Serpico himself is unsure of what to do for a good while, as he disapproves of them staying with the group at first. In fact they do leave when they get the occasion, before eventually rejoining them.
Your premise seems to be that Farnese shouldn't have been able to overcome her issues without going through a protracted process, but that's not based on anything factual. She's already dealt with her childhood trauma by the time she's introduced in the story, just not in a good way. When that crumbles, she decides to find another way. I guess you expected her to break down completely and be a mess, but she's a stronger character than that. It's what makes her interesting.
She tries to overcome her issues, and for all her defaults she has qualities too. If you want a character who ends up being unable to move past her flaws, there's Nina. By the way, let's not forget that Farnese's development wasn't over when Miura passed away. She still had a ways to go, and personally I was looking forward to it. The evolution of her relationship with Casca would have no doubt been fascinating to behold.
Besides all of this, from a storytelling perspective, there's already a character whose mental health is at the heart of the story: Casca. And then Guts himself has got his fair share of issues to deal with as well. It's simply not possible (nor would it be interesting) to spend inordinate amounts of time on every character's trauma. And I personally wouldn't read a story where everyone's a fragile little snowflake who can't overcome adversity (or a selfish asshole without any empathy).
Imagine Farnese having to become someone willing to put the needs of others before her own.
That's precisely what happens.
