I have a coming-of-age story where the protagonist has an extroverted, sociable personality. However, when plotting the story I have found that the introverted deuteragonist, which has that stereotypical shy, uncertain personality, comes off as more interesting because they go through a greater amount of change as part of their personal arc. The protagonist is supposed to go through character development (gaining direction and purpose in life), but ultimately the development comes off as uninteresting to watch because ultimately the character goes through comparably little internal change: they remain extroverted, headstrong, and sociable but merely channel that energy into a new direction. Thus, the change they go through is less extreme, and thus less interesting to readers (because readers like to see how characters made a big change from point A to point B).
I offer some suggestions.
Shift POV to the second character
The secondary character might be the better observer, acting as Watson to your protagonist's Holmes, and sensitive enough to see the primary character's flaws. Through Watson, the reader learns about Holmes' drug habit, his unfavorable opinion of women (exceptions for impeccable handwriting), and other anti-social quirks that Holmes does not consider problematic.
Adaptations tend to make Holmes a superhero, but to Doyle's credit Watson's descriptions are not Byronic or romanticized. They humanize Holmes in a way the stories and plots don't.
This might be the wrong story/medium for this protagonist
Novels are (generally) about internal conflict; films are about external conflict. Each medium flatters a certain type of protagonist and situation. Films that are "too cerebral" find a smaller audience, while novels with "too much action" might be dismissed as sub-literary. Both exist but you might need to move away from popular media to find inspiration.
Jill Chamberlain uses "Fat Tootsie" as a teaching example of a screenplay that has a situation full of comedic potential, but fails to address the protagonist's flaw. In her example, she re-casts the core conflict of Tootsie as an actor who disguises himself to get a part, all the same story beats, but without his chauvinistic flaw the situation feels arbitrary.
The story or character may need some re-consideration to make them a better fit for each other. Characters have multiple flaws, but the central conflict is probably about challenging one particular flaw the protagonist is either unaware of or over-confidant about. Nailing down that core theme might lead to the story/character you need.
Extroverts are hard
Jane Austen described Emma as "a heroine whom no-one but myself will much like.": https://en.wikipedia.org/wiki/Emma_Woodhouse
Emma is rich, pretty, and self-confidant. She does not see herself as flawed, or in need of anything. Being an extrovert she decides she will devote herself to improving the lives of others through charitable meddling.
She misreads people and motives, and she tries to fix problems that aren't actually there. She externalizes nearly every decision into a project which she attempts to implement. Her intentions are good, but of course her actions are a disaster for everyone else.
Austen uses many tricks to tell Emma's story:
Emma's meddling sees mixed results. She alienates one friend but another is happy for the attention. The consequences of both situations are not immediately obvious – at least not to Emma. Her reaction is to try harder.
Emma is immature, class-prejudiced, and even mean but without these moments, Emma has nowhere to grow. The narrator sides with the protagonist despite Emma's motives being transparently self-serving. Extroverted Emma cannot self-analyze until the 'true' situation is reflected through everyone else, which Emma does analyze. She wants to grow, but she has to put it out into the world before she can confirm the results.
Emma thinks she's mostly a good person because she has role models who are good and who like her back, but she is shallow and misjudges people by their social position, elevating one and denigrating another. She isn't social-climbing for herself but for her friends, so she doesn't see the problem. The novel proves her wrong on both. A meek introvert might not have an internal prejudice confronted, but Emma is constantly manipulating her friends to drive the plot. When things blows up it is a specific response to her own flaws.
Everyone else has something going on that Emma is not aware of. She isn't entirely responsible because other characters are never honest about their feelings, hiding a secret relationship, or reacting out of jealousy. Without an introvert's self-criticism, Emma doesn't have an awareness of why people behave falsely. She's not an idiot, but she's never needed to look beneath the surface before.
Emma has a comical amount of agency subverting her own coming-of-age story, but it's supported through backstory. She's been a surrogate wife to her father and feels aromantic about men. Emma is 'orphaned' again when her governess leaves to marry, triggering the novel. Despite all her privilege, there is a hole in Emma's life which she is trying to fill. She chooses her 'purpose' based on what she sees – women need a good marriage – no coincidence that a marriage has recently disrupted her home – becoming the marriage counselor, not the bride is a way for pro-active Emma to exert control. None of this psychology is examined in the novel – certainly not by Emma, but it feels like a very external way of working through a problem.
She has a foil, an extended-family member and mature confidant who is critical of Emma, and able to say in words what she is doing wrong. He's her external conscience counterpoint. Crucially, he tells Emma she can be more. He knows a bigger picture of the world than Emma or the narrator are aware, and he can hang a lampshade on how silly the plot is.
Emma 'punches down' at a woman of less fortunate circumstances, believing she is clever enough and the insult subtle enough to get away with. It backfires when the woman is embarrassed and leaves, awkwardly breaking up a party. Emma is forced to admit her behavior doesn't live up to her own ideal. In addition to feeling guilty about her faux pas, it's reflected in her friends making it real.
Extrovert as handicap
I think the idea is to load an extrovert with agency and turn them loose on the world. Their ideas are manifested into actions before having that introverted self-doubt. Extroverts gain experience faster through social interaction, but the answers are external as reflected by others.
Extroverts might be steered towards the status quo in affirming ways introverts are not, reinforcing cultural norms and even becoming dependent on positive feedback. Deconstructing a story conflict that would challenge that type of 'handicap' would probably involve removing the extrovert from group confirmation, contradictory group-think, or a leadership role that requires independent moral decisions.
