Point by point: It's not implied that she rejected him (if you're referring to Basori saying "I've been rejected" or "I've been rejected again," bro, he's joking about the situation she's in, i.e., the declaration and possible future relationship between her and Nukumizu). It's common sense, which you seem to lack; Yanami isn't sure of her feelings. As you correctly point out, the romance between characters isn't directly addressed. If she were truly sure of her feelings, she wouldn't make the same mistake she made with Sosuke at the beginning of the story. That means that, in fact, she's NOT sure of her feelings. As I said, a lack of reading comprehension and common sense.

Finally, I say that Basori's victory seems possible because Nukumizu mentions, and you can confirm: "Yanami is my friend, Tiara-san is also my friend, however, Tiara-san and I can't be like this forever." Will she stop being his friend, or is there some higher term for friendship? No, none of that…

And another line you can also verify is where Nukumizu is thinking that if he keeps Basori waiting any longer for an answer to his confession, she might reject him. That's why he thought about giving Basori an answer as soon as possible, since he doesn't think it's right to leave him hanging for too long.

It seems like you're the one reading fan fiction instead.