Leading characters who are foils for each other
Jane Austen's novel Sense and Sensibility uses 2 sisters as foils of each other.
One sister believes in 'sense': rational thought, measured manners, and withholding anything but polite respect for others. The other sister represents the idea of 'sensibility' which at the time was a sort of Romanticist lifestyle theory about speaking your truth, embracing honest emotions, and indulging the senses in excesses of flavor-passion-delight-poetry, etc.
Austen is clever enough to get us to like both sisters by fleshing out their dichotomy into realistic personalities (one sister is introverted and cerebral, the other extroverted and flighty), and giving them scenes together where they moderate each other in front of other characters – as opposed to clashing against each other to highlight their differences.
Together they have a chemistry that smooths out the other's flaws. One sister can comment on the other's temperament, while saying the thing the sister should have said. We see the working version of their mutually-balanced relationship, before we see their broken personalities on their own.
Showing the flaw through action
Austen does some narrative mirroring on their character arcs so we see how neither sister is right or wrong. Each digs into a bad situation the other sister would never fall for. Both hit walls where their fundamental temperaments are challenged by insurmountable dilemmas where their personalities work against them leading to character breaking-points.
At the crux of the novel, each sister is forced to find an internal moderation –– but later within the long denouement Austen allows the sisters to (mostly) return to their original personalities. Austen loves irony and double-speak, so even though big deus ex machina contrivances get the sisters with their eventual husbands, there's a feeling that life happened anyway in spite of their personalities, and not as a reward for 'fixing' their flaw.
Character trait vs Flaw
An aspect I love that might inform your story is the sisters aren't presented as 'wrong' or 'false' for having extreme personalities. The traits aren't viewed as flaws that should be corrected – but they do work as handicaps that get them in deeper trouble.
In fact all the side characters are shown to be more or less immutable in personality, for better or worse. A social climber just keeps social-climbing, a difficult mother-in-law continues to be difficult; they merely adjust their targets rather than learning their lesson. Likewise kind meek characters never speak-up, so it's up to everyone else to force their progress towards happiness.
Austen isn't preaching about becoming a certain type of ideal person, rather the story is about enjoying strong, opinionated (flawed) sisters as they mature and learn to accept the things they can't change. They're tested and have these character-stretching experiences, but they emerge as stronger versions of the people they already were, who understand themselves better.
How to double-speak?
Part of what makes this work is Austen's supremely sarcastic narrator. She describes every situation ironically, with descriptions that obviously don't match the thing being described. Every sentence drips in double-speak relating dry facts first-hand while simultaneously layered with a gossipy wrong interpretation, kind of like a comedy of a very biased sports announcer who can't admit his team is losing.
The 'truth' is never told directly, so the reader is forced to create an active composite of what is actually going on. It's established early so the reader knows the narrator is unreliable – Austen lays irony thick as a rule.
The novel gives examples of happy, mature characters who are comfortable being themselves, and don't change no matter what's going on around them. To the teenage girls these characters are presented as 'cringe' and embarrassing. Meanwhile high-status dignified characters ultimately have weak personalities shown through their actions, but the narrator flatters them according to their status.
I think the takeaway is that Austen bluntly establishes this double-speak in her language: don't trust what you read. Then she buries the stories structural ironies so they have a delayed pay-off.
Subtext isn't information withheld from the reader, it's information withheld from the protagonist – it doesn't even enter their mind so the narrator doesn't mention it either.
You've got to communicate facts to your reader, influence that meta-narrative they keep in their heads, without mentioning it directly through the narrator. The effect is that the reader is disagreeing with the protagonist's interpretation of events creating tension. (Confusing the reader does not create tension, it's just bad writing.)
The reader wants the protagonist to change, they want the narrator to confirm their opinions. By the time Austen's sisters realize the cringe elders are awesome people, the reader is already aware and it feels like a pay-off, like a release of tension.