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?