I think I've studied Emma about four times now throughout high school and uni (because of the nature of my degree) and yeah... it's an absolutely masterful piece of literature.
I think all of Austen's works are, but Emma is arguably the tightest in terms of how much meaning is fit into every line. The word play and social commentary is such a focus, I second the bit about the free and indirect discourse, and you have so much more lying and deceitful truths in this book which completely change in tone and meaning upon rereading. It really makes you question the characters and what they say or believe they know.
But what is of particular interest to me is how it explores that lower boundary of the genteel class and more than her other novels. From a historical perspective, it offers us so much nuance and information about the shifting of classes:
Miss Bates is genteel but barely clinging on because of her severe financial distress, and is reliant on her neighbours to quietly overlook the usual requirement of returning dinner invitations (she couldn't afford to reciprocate) in order to continue participating fully in genteel society.
Her niece, Jane Fairfax, is as genteel as Miss Bates by birth and far more genteel in education and manners, yet she's the one about to take a half-step down socially by becoming a governess.
Mrs Weston went from that half-step down to unquestionably genteel for life by marrying Mr Weston (himself "born of a respectable family, which for the last two or three generations had been rising into gentility and property" but was still low enough on the gentry ladder that to marry a wealthy, landed gentleman's daughter for his first marriage was a big step down for Miss Churchill "of a great Yorkshire family") who is now rich enough to have a carriage which places him in at least in the top 2% of society via income.
Augusta Hawkins is from the mercantile middle class and thus born a full step down but also moved into the gentry class by marrying Mr Elton (which is partially why she tries so hard to look the part and pushes the connection to the 'estate' of Maple Grove, she needs to establish herself in this social sphere) who, as a clergyman, is genteel but on the lower end of the scale.
Harriet Smith is in a nebulous quasi-genteel state as her education is genteel enough to allow her to mix with the gentry, and clearly someone with a bit of money is supporting her, but she's illegitimate and therefore can't fully be placed until her family connections are known (because she would naturally be lower than them) unless she happens to marry first and thus assumes her husband's position.
Mrs Goddard was likely a governess or teacher in her youth, genteel enough by birth to educate young ladies, but poor enough she had to work, and's now the mistress of a school. Which makes her less genteel than Miss Bates, technically, but with more financial freedom. And it's a respectable enough career that she hasn't been completely cut from Highbury high society, though she exists on the periphery.
The Coles are a merchant family whose wealth is allowing them to takes those steps to move up the social class (via the education of their children and hosting the local gentry) and we see those tensions in the novel and how delicately it had to be balanced (Mrs Cole couldn't just invite the Knightleys and the Woodhouses to dinner, her husband could befriend the local gentlemen freely but Mrs Cole was first friends with the lowest on the genteel scale, Miss Bates, and had to slowly establish herself socially before making an overture towards Emma).
The Martins may be what Mr Weston's family was two or so generations ago, especially if Robert Martin ever buys the farm he rents from Mr Knightley (which would also put them on track to be like the Hayters from Persuasion), and are also becoming more respectable and educated. They're not moving into the gentry class yet, the Miss Martins are too securely lower class to have tea with Miss Woodhouse even though they've got the same education and perhaps greater wealth that Miss Smith, but Robert Martin is already starting to mix equally with families along that genteel border, like the Coxes, though he and his sisters are not high enough to be invited to the ball. It's an interesting contrast to Miss Bates, who is poorer and less educated than them, and yet unquestionably genteel and invited where they are not.
Then the Coxes themselves are "very vulgar" but their son, William, is a lawyer (perhaps his father too, and likely 'only' an attorney, given he seems to have an office in Highbury - so not nearly as impressive or genteel as Mr Knightey's barrister brother) so we might think of them as the same social sphere as Mrs Bennet's father in Pride and Prejudice and learn more about her status before her marriage from that.
Though Emma and Mr Knightley are the main couple, and are both far above the border of gentility, the majority of characters in the novel are not. And a lot of the tensions between characters are caused or exacerbated by minute class differences. Emma's treatment of Miss Bates is so dangerous because it could set the tone for the rest of Highbury and result in Miss Bates being shut out from genteel society since her position is already so tenuous, aside from Emma not wanting to marry Elton she's offended he would even aspire to her, and is extra offended his wife considers herself Emma's equal, Emma wavers over accepting the Coles rise or opposing it by declining their invitation, her desire and attempts to secure Harriet's as genteel causes many problems for them both, her shunning of Jane Fairfax as a friend gains an extra layer of insult when you understand that she's the suitable and natural choice due to her class and education, and Mrs Elton being patronising to Jane would've been even more unjust to contemporary readers than us since they knew Jane's 'naturally' the social superior by birth.
You lose so much of the novel if you see it only as a slow burn love story and not a deft study of blurring class lines, the resulting tensions, and the difficulties of maintaining and risings ones' status. None of Austen's other novels let us see so clearly the influence and importance of wealth as opposed to birth and education on class. (I actually have an essay about that topic in Emma, lol)
All of Jane Austen's books offer social commentary and explorations of class as well as studies of human character, let alone amazing wordplay and pioneering language style, but even among them Emma stands out. It's not my favourite to reread, or my favourite couple, but it's such a masterpiece of literature and I love it dearly.