I'm seeing many believe that this version of Nano never met and fell in love with a version of Rentarou... what if its not because she
didn't, but rather because she
did.
Think about it, the multiverse is a vast place, and every theoretical possibility exists. For all we know, the soulmate clause
wasn't in effect in this universe, so what if this is a world where either Rentarou
died at some point, or this Rentarou was a jerk and broke Nano's heart, with this version of Nano being so cold and efficiency focused out of poor attempts at coping with her pain.
This wouldn't be the first time after all, as all of the previous "serious" arcs focusing on the initial girlfriends had the negative emotional moments stem from grief and poor attempts at emotional control.
- Hakari's arc: Hahari was forcing Hakari to break up with Rentarou out of fear that Hakari would end up like herself, someone who does reckless things out of love like she herself did when she had Hakari so she could always remember her late boyfriend, and never properly processing her grief. She relents when she sees the genuine love Rentarou and Hakari have, as well as Rentarou promising to be there for her too, allowing her to be more open and unrestrained.
- Karane's arc: Both "Tsundere Lost" and "The Inda Family Secret" stemmed from Karane's self-loathing of her tsundere traits, the former thinking it made her lesser than the other girlfriends due to her always hurting Rentarou, the latter out of worry Rentarou wouldn't want to have a child with her if that child would be a tsundere as bad as her, both cases having Rentarou reaffirm his love for her and how her being tsundere is both a charm point for her since its her genuine self, and that any child they had together he would love no matter what.
- Shizuka's arc: Shizuka's mother abusing Shizuka was done out of very poorly thought out sense of trying to help Shizuka "fit in" with society, thinking society would never accept her due to her mutism, but Rentarou managed to make her see she was just imposing her own will on Shizuka rather than actually listening to her, Shizuka herself actually talking albeit with great difficulty to convey her own desires, causing Mrs. Yoshimoto to finally realize she was so worried about how others would treat Shizuka she had stopped thinking about Shizuka's own desires, allowing her to slowly mend her relationship with Shizuka like teaching her how to cook and accepting her relationship with Rentarou... even if she thinks their kissing sessions go on for too long.
So it would make sense for the antagonist of Nano's serious arc to be undergoing something similar, and her embracing efficiency out of
heartbreak would fit.