The drama regarding Nagi and the fiancee will only lasts about 5-6 Manga Chapters (Chapter 14-19/20) based on the pacing so far.
Chapter 16: Souta Minori (MC) will head home by himself after Nagi leaves the date after the Ferris Wheel ride, and will talk with his best friend regarding Nagi's fiancee and her cutting off all communication. His friend will ask him "are you really okay with this?" and MC will realize he's NOT okay with this and decides that he will head to Nagi's house the following day.
Chapter 17/18: Souta Minori arrives at Nagi's house in the morning and encounters Nagi's father and explains that Nagi will NOT be happy with this arranged marriage. The father realizes that Nagi is actually in love with Souta, but she has never told either parents that Souta even exists (both parents believe Nagi has no male friends). Nagi's father apologizes to Souta for accidentally forcing Nagi into a situation where she believes she has to accept this arranged marriage, and tells Souta that he will be cancelling this arranged marriage.
As all of this is happening, Nagi and her mother has been outside the room, both overhearing the entire conversation between Souta and her father, and both finally decide to enter the room. The parents explain to Nagi that the reason they brought up this arranged marriage was because they thought Nagi struggled with talking to boys, and hoped this arranged marriage could help her overcome her fear. They only brought it up because they didn't know Nagi was already talking to Souta and was already in love with a boy. After a bit of back and forth between Nagi and her parents, Nagi's foster father reaffirms they will be cancelling this arranged marriage and leave the room to allow Nagi and Souta to privately talk. The two make up and reconfirm their love for each other, and both CLEARLY state they want to be with each other forever (including marriage).
Chapter 19/20: After their talk, it's now roughly lunch time, and Nagi and Souta leave the Nagi household to meet up with their friends (since Souta Minori came to the Nagi's household with their friends who are waiting outside the house). Nagi and Souta thanks all their close friends for helping them realize their true feelings for each other and they all hang out for awhile before the friends finally head home for today. Before leaving the household, Nagi took with her a giant backpack filled with clothes and other living necessities, but didn't explain to Souta what was inside the backpack. Now that their friends have headed home and the two are alone outside, she essentially "forces" Souta to allow her to stay over at his apartment for tonight. The two end up kissing, cuddling and sleeping in the same small bed tonight (no s3ggs).
Unfortunately, their first time having s3ggs together will happen the night after New Years, after they return to Souta's apartment after visiting Souta's parents for New Years. They were actually about to have s3ggs at Souta's parents home, but decided against it since it would be inappropriate to have s3ggs while his parents are literally sleeping in the same house. Based on current pacing, this will probably happen somewhere between Chapter 25-30 of the manga.
Note: After this drama arc, Nagi and Souta Minori's relationship is pretty much full out-in-the-open, and they constantly say "I love you" to each other, both in private and public, as well as hold hands/arms, and kiss each other practically every chapter (sometimes it's actually a bit too much, but very wholesome). Nagi even immediately calls out other students when they shit talk about Souta, saying things like he's not good enough for Nagi. This is a very nice part of the story since they don't try to hide their relationship at each other's schools (fuck that romance trope).
