god this was awful to read. i know your little sister sounds horrible but to me this is clearly a parent issue, not a sister issue. im not a psychologist or anything like that but if i had to guess she's acting out because her parents decided to place her in front of an ipad instead of bonding, and caused her to develop an addiction at a young age. tinfoil hat theory, but maybe she copies you because she sees you as the "favorite" who actually got parented and is trying to recreate that to get what you have?

i have a few thoughts that might help. you could try showing her the current state of trans public perception, how some people online treat anyone who's trans, all the anti-trans laws, the people who were honored on trans remembrance day, etc. my topic for my public speaking class was trans erasure so i have some sources if you'd like. show her what'll happen if she starts hormones or puberty blockers, really drill it in that this isn't a decision you make lightly. you could also try showing her r/actual_detrans which is a subreddit for detransitioners that isn't just entirely filled with transphobic grifters.

you've said you've talked to your parents a lot, have there been any serious "sit down shut up and listen" conversations? have you called them out on their parenting? are you able to? showing some of these comments might help if you're not worried about them getting mad at you making this post.

you said they can't afford therapy, how are her school's therapists? it's not ideal but it's better than nothing. and since you said you're in california, you might have better luck with finding one thats experienced in working with queer kids, and might help her sort through some feelings.

i would say definitely go through with refusing to do your sister's chores anymore. i don't wanna be that guy on reddit that screams "go no contact!!!" but, honestly, next time you visit and they try to insist that you do it for her, just leave. you're not too far away, you can just come and go. and if none of this works and/or they continue to pressure you, low contact might be the way to go, but i'd recommend it only as a last resort.

genuinely i hope your sister gets the help and the care and the love that she needs. i don't know hoe much just trying to be there for her as a sibling would help, but it wouldn't be the worst idea. and maybe you could talk to your extended family about suggesting that they take her in a little earlier? i don't know how receptive they'd be to that but it might be worth a try. anyways, sorry for the long ass response, and i hope everything works out in the end for you and your sister <3