Erika not only doesn’t have a problem with Nagi confessing to Hiro; she wants to help him, unaware that Hiro is engaged (since Nagi doesn’t share that detail). She tells Nagi that Hiro “putting him on hold” isn’t the end of the world; if she truly didn’t like him she would have summarily rejected him.
For their first study session, Erika and Nagi arrive at school at the same time despite taking different modes of transportation, and despite Erika dressing up like a literal cupid, Hiro can’t help but notice how close the pair seem to be. Erika and Nagi themselves aren’t aware how good they are together!
In an effort to catch up (and eventually beat) Nagi in a contest of with whom Erika is closest, Hiro invites herself over to Erika’s house. She diverts Hiro to her parents’ house, which Nagi believes puts him in the clear to have a nudist evening with their house all to himself. However, Erika’s parents’ house is “being renovated”, so she has no choice but to bring Hiro there.
It’s a classic sitcom scenario in the mold of shows like Fraiser, with Nagi not only having to remove any evidence that he lives there, but spend most of the time hiding around the corner naked. Erika does her best to keep diverting Hiro, but then things get even more complicated when three of Erika’s stalkers show up at her house. Thankfully, Nagi dispatches their leader with ease, and without being detected.
Ultimately, it’s not just about being caught for Nagi. He genuinely wants Erika’s first friendship and first houseguest to go well. That plan is almost torpedoed when Hiro finds his shrine stamp book on the counter, but Erika is able to explain it away as having borrowed the wrong book. This, of course, only confirms to Hiro that Erika and Nagi are very close.
Her solution to that is to invite Erika (and fellow study buddy Nagi) to her house, which turns out to be a huge shrine. Shrine Maiden Hiro is indeed cute as hell, while Hiro’s mom is extremely prejudiced against Nagi, giving him only a small hard candy while Erika gets a delicious-looking jelly roll-like confection.
Nagi does get a personal shrine stamp from Hiro, who demonstrates that her stamp game is far better than her regular handwriting. When Erika goes to the bathroom, she asks Nagi if he understands now what she meant by “engaged”. She isn’t promised to another man, but is poised to inherit the shrine.
Why that should mean romance is a no-go when—well, she exists, which means her mom and dad had a kid—I don’t know, but Hiro doesn’t want to burden Erika with such a “heavy truth”. As for why she told Nagi? She thought he could handle that burden. He may be “on hold” indefinitely, but that doesn’t mean she doesn’t like and respect him.