i really like this question. i hope you dont mind that im going to write a short essay in response

if jade understood that saving ichors life in the way that she did would cause ichor to form a cult based on her obsession with her (a cult-cult, not "cult" in the ancient greek way like the cult of the witch already was), she still would have saved her, but wouldnt rely so much on ichor Being Normal About It afterward. i think jade believed that ichor was so rattled from nearly drowning that perhaps she wouldnt even remember that the witch of space saved her, or maybe she would convince herself that she imagined it during a near-death experience. unfortunately for jade, ichor was raised by a society that dedicates itself to the protection of jades mortal, pedestrian life. she knows the witch walks among them, and where she lives, as all coven members do. so there was no hope that jades good deed would go unpunished

ichor is so un-normal about this event solely because she is already a pretty tormented soul by the time it happens. she is relentlessly bullied by a group of other children in the coven, and generally feels like she doesnt belong. morgin casts an unsympathetic gaze upon her too, viewing her as a failure even before she defected. if ichor was well-adjusted, she would have cherished the memory of jades rescue as a blessing she didnt deserve, but then again, she wouldnt have been kicked off the bridge to begin with! because ichor already feels ostracized, she latches onto this event as proof that she is meant for something greater, and that the witch of space will divulge her divine secrets to ichor if she proves herself useful and faithful.

so, why would jade feel compelled to save her? first of all, shes a child, shes not going to passively allow a child to come to harm. but beyond that there is a tragedy to ichors character that i feel jade can understand. jade is not a character whos feelings are taken much into consideration throughout her story. she largely exists to fill a useful role in the journeys of characters around her. she makes the metaphorical chess pieces move, she allows for events to transpire, she helps people come to realizations, but however interesting her backstory is, no matter how rife her potential is, it isnt treated with gravity. ichor, too, has lived a rich and strange life in her pursuit of the witch of space. she was raised by a secret society, she was saved by the random whim of a god, shes bound multiple cult fortresses together through sheer charisma, she goes through the effort of CODING SBURB AGAIN to correct the course of a history she believes is wrong. but we dont get to see any of that. not just because the cult of the witch/flayed wolf was always historically the least popular aspect of KQs story, but because ichor herself matters more as a lesson than as a person. the tragedy of ichor is that she serves the sole purpose of showing the originators the harm they are capable of inflicting on their worshippers even if they choose to remain anonymous. early in the story, kitty asks if being a god makes you kind of selfish. and by the end of ichors arc, that answer becomes a resounding yes. ichor has dedicated her life to molding her god into someone she feels will reward her devotion. she says its for the betterment of society as a whole, but this is not entirely emotionally honest. and how is she rewarded? getting her memory wiped to protect the comfort of jades family, which leads to complications severe enough to land her in assisted living. when i was writing jades conversation with vrisrezi, i half-wrote jade gradually realizing that ichor was the girl she rescued. but this didnt feel right, and it got scrapped. how agonizing it is for ichor to carry this memory with her throughout her life, but for jade it was just a tuesday. if i ever entertain the idea of continuing KQs story, i definitely want ichor to get her vindication somehow

im sorry to put my "raised catholic" hat on again, but ichor is really like, an anti-moses. when i think of her arc, "impotent, directionless rage" comes to mind. which makes her the perfect final boss for an awakened kitty, who has to learn where to direct her passion as she grows into the role of the mage of rage

so yes, jade would rescue ichor because she sees in her the unfulfilled, chronically lonely child she used to be. but she would have taken more care in the act of saving her. i could see this going two different ways. on one hand, maybe shed just make sure ichor didnt get a good look at her. maybe, though, she would sit down with her in the grass and wait until she was steady enough to get back home. maybe she would talk with her, answer all her questions, entertain her curiosity, and the two would come away with a mutual understanding. maybe ichor would have put more effort into her studies, carried herself taller with the knowledge that the witch of space gave her a second chance at life, wouldnt have defected. jades not a seer, though, so how was she supposed to know?

if roses light powers were still useful outside of sburb, i wonder if she would feel the strings of fate pull taut when jade pulls ichor from the river. jade comes home to a voicemail thats essentially like (jake the dog "dude, lets kill the horse" voice) "dude, put the kid back in the river"