Oh, it’s such a good thing that saying “I’m in love with someone” to the actual person you’re in love with can’t possibly be misunderstood by the person you’re saying it to, because if they were secretly in love with you they might think that you meant someone else who is not them and then they would feel bad but would probably still decide that they needed to support you in your love for someone else even though they would be secretly heartbroken.
And we wouldn’t want that to happen.
Honestly, I think that's the point, as Yuzu is so far up her own neurosis that the only thing that will get through to her is a heartbroken best friend confiding on her. Minami has tried confessing and got flat-out rejected. Hard. In such a way that could not be mistaken.
That said, Minami does deeply value her friendship with Yuzu, so after an entire day together where she knows she wasn't hiding her heartbreak, Minami does what she would have done with any other issue: talk with her best friend about it. The fact that Yuzu was the one to reject her is completely irrelevant here, Minami never wanted her love for Yuzu to damage their preexisting friendship, so Minami is seeking support while stripping away the context of the romance.
Maybe Minami will mention that the person she was in love with was Yuzu. Maybe she won't, or will only do so reluctantly if Yuzu jumps to conclusions about who Minami was in love with. Regardless, from Minami's perspective Yuzu doesn't need to know that she's the cause of the heartbreak. She just needs to know that Minami is heartbroken after asking someone lose to her out, and getting rejected.
That said, I do somewhat hope that Yuzu gets really upset at the implication that someone close to Minami left her heartbroken like this, and demands to know who just so she can give her a piece of her mind.