Okay, this is just a gag manga I guess.
It's weird she's concerned about Yuku being loved, when the current evidence clearly favors her already.
It definitely feels like there's no real stakes to what's going on.
Even concerning their personal bet over which of them was more loved by Kazuomi, I feel like there's little to no gravity behind answering it.
Especially as both are arguing in favor of the other; feels very self-deprecating, given "winning" just means confirming you were the "other child". But it's not like someone gets disinherited (since Naoomi's being denied anything at all by Yukari), or like there's some other big risk on the line.
I guess it's potentially just a fake-out plot from the author to obfuscate the alleged deeper narrative that Yuzu isn't actually Kazuomi's daughter, and that Yukari is hiding her own affair/other relation; but the way all the mini-mysteries have been resolved up to this point just makes it hard to care about the supposed severity of what's going on in general. If it turns out Naoomi's the only legitimate child of Kazuomi, then all that amounts to is that readers predicted the Big Reveal by the second chapter, and everything else is just waiting around until the author catches up. It wants to be a mystery series, but it's more like gag/romcom with fake incest undertones that I do
not expect the author to stick to (unless every flag described by others in these threads about Yuzu's true parentage are
all false flags). Everything else is just...not really on-theme to what's described, Tags-wise.
At this point I'm kinda waiting for the harem routes to start. Either for Naoomi, or for Yuzu, though I'd argue it would be Naoomi pulling the heroines given we've been getting more of the "Yuzu's caught feelings" nods than anything from Naoomi's end, as of late.