Anything familiar or has the timeline change completely displaced opera he's heard of?

One of them does have a name and many plot elements in common with one he's heard of.

Well, he's not going to let on he's familiar, he doesn't want to explain how it made it to Narnia, but it's nice that some things are the same.

Eventually, someone announces that all should rise for the king, and the ballroom gets mostly quiet as the king comes out and sits on a rather plain-looking throne. Each debutante is then brought in and presented to the king, with a man reading off their names and titles before they curtsy, the king nodding after each, dismissing them. Most members of the ballroom watch the debutantes do this, whispering amongst themselves about their suitability for matches.

God, these poor girls. Haru had never before considered how load-bearing it was to the relatively low rancidity of the dating market that people could just be permitted to fail at pairing off. Someone in this society is the worst human being on Eighteenth Century OK Cupid and someone still has to marry them.

Lucette is accompanied by a distant cousin rather than her own mother. She dips in an appropriate courtesy, having practiced exhaustively given the stakes.

He should ask Lucette later if there is a technical reason gay marriage wouldn't work. She could marry Lady Brynd and they could talk about the weather and not have any children slated for routine torture.

Unfortunately, nothing so far indicates anything not strictly heterosexual as an option. After the presentation, the debutantes are free to mingle, each holding a dance card for men to fill out to reserve one of the ten dances that will be occurring later in the evening. Lucette has hers signed by three different men by the time she makes her way over to Haru.

"Hello there. Shall I take one or two of those?"

"Two would look presumptuous coming from an unempowered, but I would be grateful for you to take one."

He signs his name next to the fifth dance.

"I also have opinions on other people you should dance with, for political reasons, if you are up to navigating such interactions."

"Do tell."

"I think the most promising way to gain the favor of the Duke Metcalfe requires that he distrust the assessment the Lord Metcalfe might provide of you, which seems doable given that he had to bail Lord Metcalfe out of some trouble not too recently, according to one of his friend's sisters. And so it might be wise for you to dance with Miss Henrick, Duke Metcalfe's favorite niece, as well as Miss Anderson, Lord Metcalfe's former ...interest, whom the Duke Metcalfe did not approve of for reasons I won't bore you with, in hopes that this will taint the seriousness with which the Duke will take any aspersions cast on you by his son. Also, if you'd dance with Miss Haster, it would help me by way of a complicated chain of relationships and reactions that involves a besotted habberdasher... I regret not having my notes brought, though I suppose I couldn't be seen going through them anyways." 

Lucette gestures discreetly towards each young lady as she names them.

"The tall one in the pink, the blonde with the ribbons, and the one in the lacy blue dress?" he checks.

"All correct."

Then he will wend his way to these targets and seek to sign their cards.

Based on how other men are doing this it requires flirting with each woman first.

Oh god. Fine. "Good evening, Miss Henrick, how does this ball find you?"

"Excited, though I dare say a bit nervous as well. And you Mr. Swan?"

"I'd imagine your nervousness misplaced, I'm sure you're an accomplished dancer. I myself am little acquainted with this sort of ball but hope to acquit myself on the floor tolerably well; I've been catching up on English dances."

"Oh, have you had the chance to learn the minuet?" Miss Henrick gestures as she asks her question, drawing attention to the dance card tied to her wrist.

"I believe I can perform a minuet, if you'll give me the opportunity to demonstrate?"

"I'd be delighted." She holds out her hand with the dance card for him to sign.

He'll find a slot that is, ideally, a minuet, and not #5, and sign. "I shall look forward to it," he says, bowing over her hand.

And next.