@givemersspls You missed a subtext in the lines Bandai was communicating in her speech. I would start my explanation with a really good picture I once saw of the same trope, but I can't find it. So I have to make due with
https://static.tvtropes.org/pmwiki/pub/images/jokermourning_8002.jpg. It's not as good as the one I would like to link but the meaning it is suppose to invoke is close enough - even while being enemies, the fight was never about achieving victory, it was about the rivalry.
In terms of tropes, it's an academic version of the trope "
https://tvtropes.org/pmwiki/pmwiki.php/Main/TheOnlyOneAllowedToDefeatYou" and
https://tvtropes.org/pmwiki/pmwiki.php/Main/AntagonistInMourning where in the trope implying a respect and attachment reserved only for a worthy rival. These types of tropes is always presented in a double layer message. The first layer is the typical words of animosity, yet by the way it is worded and context, a second layer is implied - a layer implying respect and attachment.
That was what
@Logic and
@Wnf saw. And why they were confused by your post.
The lines "My 495 beat your 482", "the English Quiz was also a 10 vs. 10", "I won 97 times and we have 120 draws" was not suppose to mean an over-competitive mindset, but an academic version of lines used between rival warriors in those historical dramas or lines between two heated, yet respectful rivals in a sports anime. Sames goes by the lines about "but if we were competing over taking care of ourselves, I would have a flawless victory", it not to mean she is making health a competition, but an expression of her wish he takes care of himself better.
Using the framing of their rivalry, she is poetically framing that she wishes to continue facing him at his best implying she views him as a worthy opponent which in this context also means some romantic implications.