Sure the reply letter is just a mistake of her writing book translation in there. But from outsider POV, it definitely what they think of their relationship.
Exactly lmao, she may not have been thinking of him when she wrote it, and may not have intended to say it to him in so many words, but isn't it completely true of her feelings? If someone shows her the letter and asks her if this is what she really thinks about Keios, wouldn't she just say "Yes, I suppose it is"? It's a funny sort of misunderstanding trope when the mishaps and hijinks result in everyone coming away with a
more accurate understanding of the situation.
Not to mention, Keios may insist he genuinely loves her, but can you genuinely love someone and still not care if you see them for months on end? I'm still not completely convinced that he doesn't see her as more of an accessory after all, just like the man in her book. No wonder she finds those books so compelling, she must find them very relatable.
And even after all this, when Keios knows exactly how thin the ice has gotten, and that he really needs to pull out all the stops to win her back, he still needs to be
told to invite her to the next major social event. What an absolute chump.