Like I said in previous chapters, contrary to what a lot of people think, I think Nanao truly loves the mc and that she's a kind person. Sure, she would be up in the competition if Amane is discouraged and sad but she doesn't want that. She would go out of her way to lift her rival up because...
It even gets to a point where people in here think she doesn't actually like the mc... Like come on are you even reading the manga? Not to mention, I act exactly like her when I have someone I like.
Her helping out Amane is something I can relate to as well. Sure, making someone depressed and...
I forgot to say this but nanao might be doing this out of pure love for the mc. She might want him to know that all those beautiful girls like him and not just her. Then let him choose which one of them makes him happy. Like, she just wants him to be happy even if it won't end up being with her...
This is like when you're winning at a moba game and instead of going for throne, you back and let the enemy farm to make things more challenging (or see them struggle more)