When Erika takes off to hang out with her mom (the one who raised her) Sachi doesn’t waste the sudden opportunity to hang out with her Onii. She ostensibly wants to buy a gift for their mom, but both of seem to agree their mom isn’t much of a gift receiver, so you have to think part of her just wants to see what it’s like to go on something like a date with Nagi.
The two settle on an apron (and sure enough, their mom could take or leave it) but when Sachi comes upon the idea, Nagi rewards her with a head pat, which pisses her off to no end. As much as she pretends not to stand him, Sachi wants Nagi to see her as a girl, not an imouto. Alas, he’s utterly oblivious. He just wants to study and win Hiro, which is why he’s probably none too pleased about suddenly being yanked out of the house by Erika.
Erika, who herself was blissfully reveling in her first cup ramen, got a text from her dad saying he’s coming—no discussion, not argument, he’s just coming and that’s that—so she ditches both wallet and phone, grabs Nagi, and heads out. Where doesn’t matter; that even she’s not sure is the point. No GPS or purchase history means even someone as rich and powerful as her dad can’t find her if she doesn’t want to see him.
Instead, Sachi is person who encounters her dad making himself at home in the house. She initially thinks he’s a burglar, but she should have called the cops anyway, considering he later lures her out and plys her with foie gras. I’m with the wait staff of his restaurant: it’s weird that he suddenly takes Sachi out to dinner.
Sachi is there for the foie gras, and also considers it equitable to tell Erika’s father about how she and Nagi are getting along. She probably doesn’t realize she’s being a snitch, because she’s distracted by the fact this is another opportunity for her: if she says they’re terrible together, she could potentially be able to swoop in and have Nagi to herself (again).
But Sachi is not a bad person, so she tells Erika’s father the truth: as mismatched as their personalities seem, Erika and Nagi definitely have a spark—je ne fois gras, if you will. Their chat is interposed between scenes of Nagi showing Erika a good time with zero yen thanks to a steep hill and a piece of cardboard.
As for Erika’s increasingly creepy dad, he heads into his office to admire a framed photo of him and Erika’s dad with Erika…and Nagi, looking like older toddlers. This is strange, as my understanding is they were separated at birth; this suggests they were reunited at some point. It also gives credence to the fact the “certain someone” Erika is trying to reach through SM is, in fact, Nagi, and the two of them simply somehow forgot they knew each other as kids.