She seemed interested in both of them, no? At least that's how I interpreted the "they're so my type" thought bubble. Maybe she just wants to join them, polyamory style. Though I'm not sure how that would work out, because it seemed like the story was just going for the tomboy x tomboy dynamic, actively crushing Haine's dream to get a yuri harem.
Well we don't know which person she initially thought was a girl and who was "her boyfriend". If she first saw Haine, that's one thing, because
that would play into Haine's desire for a yuri harem. If she saw Shizu first, then she's automatically a threat to Haine, who wants Shizu to fall for her and is upset that Shizu is instead competition for other girls.
Another girl falling for Shizu goes against Haine's plan.
But if she were to go after Haine, that could affect Shizu who has been opening up in the face of Haine actually seeing her for *her and treating her like a true friend instead of an object of beauty like all the other girls. This chapter's a great example of just that. A girl seriously chasing Haine could be what makes Shizu realize that she wants Haine for herself, and result in her solidifying her own feelings/see them develop toward in a more concrete manner.
Regardless, she's going to interfere generally with Haine's initial desire
and the actual plot that's playing out between Shizu and Haine to this point. Haine may want a yuri harem, but as you indicated, what's being telegraphed this whole time is a tomboy×tomboy story between the two of them. A third character being introduced into the foreground/forefront like this (because no other character has, to date) will affect that significantly, making her read more like a rival than anything, at least initially.
I originally said I was doubtful mostly as a meta call, in that the author would go against the grain and not take the formulaic approach. I have nothing to back that up, however, and she might actually be there to initiate a Triangle Plot to push Shizu and Haine closer together by way of jealousy or threat of interloper.
But I hesitate to jump straight to poly being the answer because that's distinct from harem—and without knowing the author's other work, "poly" is rare enough in manga that I don't see it as an obvious answer, especially when she's being introduced well after Haine and Shizu
and is showing up at the tail end of a date acting like she's carrying the "Rival flag".