I don't know if this is just a me thing, but the way Yamato speaks during this scene makes it sound like he doesn't know Takeru is writing a novel about their adventures.
Depending on what you want to believe, Takeru either starts writing his novels of their adventures either after 02 ended or some time around Tri, but both are before LEZ takes place. Takeru even says that he's spoken to the others about their adventures to make sure he gets everything right(this was said in his 02 spring story).
However, this makes it seem like Takeru either doesn't do that(it is an audio drama where he says he talks to the others in 02 so canonicity can be questioned) or he just hasn't asked Yamato about it. Taichi even seems shocked to hear Takeru is writing a novel, so has Takeru not spoken to any of the older kids about his novel or whats it about. Or in this movie, are they retconing the audio drama and stage play as both having questional canonicity and saying Takeru starts writing his novel in college? All of these options are weird to me.
Nothing says Takeru has to write everything in chronological order, so maybe he just hasn't gotten to his original adventure, but I also don't think he'd skip it for this long. There's also nothing that said this couldn't be a different novel. As even though nothing canon supports this, many people myself included think he also writes novels about other topics and in other genres.
Again, I could just be interpreting what Yamato says wrong, but this is just what I thought about when I first saw this scene. There could also be another piece of media that explains or expands on this that I just do not know about. Also, Yamato sounds annoyed and upset when he says Takeru hasn't let him read his novel yet, and I love that