I think Aya said onii-san simply because Mitsuki was in her shop clerk getup that initially fooled Aya. She was reminiscing about how awkward she was back then compared to Kanna and Joe.
My guess is more that Aya doesn't think of herself as gay and, at least on a physical level, is more atracted to Mitsuki's casual look, so when she thinks about her in a romantic way, she tends to revert back to thinking of her in the context of "Onii-san", or at least that part of her persona, even though she now knows Mitsuki is "Onii-san" and she likes her for more than just her looks. So, in this chapter, while she was watching the adults flirt, she thought it would be nice if she could do the same with Mitsuki, but when asked she absentmindedly blurted out the wrong name, because that was the context she was thinking in.
Alternatively, Aya has a tendency to get easily flustered when Mitsuki accidentally turns up the rizz, which tends to involve the "Onii-san" aspects of her persona, and Aya was thinking it would be nice if she could flirt back. Of course, admitting to your crush that "I really wish I wouldn't immediately melt down when you're being extra hot" can be pretty embarrassing, as can admitting that you find a part of their persona extra hot in the first place. Also admitting that you're drawing parallels between your interactions and the way the ex-couple across the room interact. Aya, basically just did all three of those things, realized what she did, and then panicked and ran.
The more I think about it, the more I think it's the latter, especially with the "perceptive girl × oblivious girl" tag at the end.
