In Sana's first dorm event, she talks about how she "let you inside" supposedly referring to Sensei, but we're explicitly told that she says it while speaking to a white rabbit.
I skimmed through some other events, and while the rabbit is visible in the background sometimes, it's only prominently placed in frame two other times (that I found). Both times, Sana is masturbating.
To me this is pretty clear indication that the white rabbits belong to Pareidolia. He's been fucking with Sana and is probably responsible for turning her horniness up to 11. It also makes nice thematic sense: HOPE = light has black rabbits, so Pareidolia = dark has white rabbits. (Plus she has spider stickers on her wall that are mentioned in the same event where the rabbit is introduced).
Very tangentially related: what is going on with Sana's hidden eye when she gets possessed in "It Comes to Claim Us All"? It looks like there's something there some of time, even when her visible iris disappears. I'd chalk it up to oversight, but the bit we see is also black instead of green. Am I seeing something wrong and this isn't her iris/pupil? Is there some weird Koikatsu thing that would explain it?
Yeah, that's something I've thought about posting before. In "Mysterious Abundance of Chickens" and "To Die To Sleep" there is a white rabbit in the alley. In "First Contact" it's now a black rabbit. I haven't been able to come up with any idea for why it changed.
The white rabbit in the chicken alley is consistent with Pareidolia, given the assumption that he's the one waking SeKaori. SeKaori wakes for the first time in "Mysterious Abundance of Chickens" in the alley, and for the second time in "Clouds," which occurs directly after Sensei and Kaori go to the alley and to the maid cafe, which also has a white rabbit. On the other hand, you can probably make an argument for anyone else being connected to the chicken alley as well.
One more white rabbit that I just remembered: there's one on top of the fridge in "Times New Roman", which is Pareidolia's reset event.
I think the purpose of the rabbits is as observers, I just think the color indicates who they're observing for.
I don't have a good explanation for the blindfolds yet, but I don't think it can just be a HOPE thing. I can't see any way that HOPE would be involved with the blindfolded "What's "A" Stand For?" rabbit, and I also find it pretty unlikely he's connected to the Abandoned Shrine. I would also be annoyed from a narrative perspective if the rabbit color is meaningless after it's been established that all of HOPE's (known) rabbits are black.
In theory: the pupil and Sana going in and out of possession could hint at Pareidolia not being as effective at possession as others.
Notably, after that Event:
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Pareidolia shows up, introduces itself, and "helps" Sana in:
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While she's seeing things and USER1 is seemingly Account Sharing:
Which may imply that something can hack into the stuff of other USERs/gods. Pareidolia seems like the prime suspect considering at least one Narrator fears it, and it's notably able to do what others can.
Anyway,
the what is "A" for thing:
And blindfold could imply that the white Rabbit, is related to The World Itself, who seems like natural opposition to HOPE and Yasu.
Sekai and Nozomu "together in death as they were in life" could imply these two entities are connected. Nozomu translating to Hope and Sekai to World. Both entities also seem Summer loving, and Angel using. HOPE seems to use white Angels and black Rabbits, so perhaps The World Itself uses black Angels and white Rabbits:
Vs
That what is "A" for, under a white Rabbit seems reminiscent of Sekai's alphabet song from her 'Something Everyone Knows and Ignores' (S.e.k.a.i) Happy Event, which the plants have brought up before:
Not to mention, A might be Apple, and considering the whole this sex-world is a fruit from a god tree thing:
It might be a very roundabout way of connecting Sekai to the world through an Apple (fruit from tree) and the letter A. There's also that poem that mentions an apple in the Chapter 2 'Glued to the Sky' Main Event, that has Noodles the Bird and the Shapeshifter/Himawari hanging around it.
As for the reason the white Rabbit is sometimes blindfolded; it isn't entirely clear, but it could be how the supernatural beings transfer info and, in Sekai's case, could be related to peekaboo:
Overall: The white Rabbits seem related to Sekai/The World Itself. Although, Pareidolia may be involved anyway. They may even be one in the same, or simply working together
Btw, presumably that same white Rabbit from Reset6 showed up again later:
So basically Doki-Doki's Monika?
Ami definitely at least seems inspired by Monika:
Plus I'd be surprised if these girls aren't aware of that game or characters, etc. A lot of them are anime/manga/game lovers. Maya seemingly being into darker and weirder stuff.
Edit: Albeit in retrospect, "Monika" could be Sekai, and Ami is simply her kid. Or if things go back far enough, the original "Monika" could be Saki from
'Nothing is Beautiful', with Ami being her granddaughter, Sekai her daughter in law, and Sensei her son, all being somewhat sentient fictional characters or simply thinking they are as part of their characters. I do hope Sel spices things up if it truly goes down the Doki Doki route.