It's normal for new cats to relapse. Give her time. Did you put the litterbox in the bedroom?
More to Birman than Persian IMO.
I don't have any experience on this. Did you bring your cat to vet yet? I just read about this just now, depending on the severity, change of diet is needed, cat food with higher fiber. Did you try that? Better ask vet for better advice.

She may relapse from time to time. It's normal for new cats, especially kitten but she eventually stop doing that. I think you know the faster solution, put litter box (or another litter box) in the bedroom.

You can consider SmartSift litter box if "eeww" factor is a concern. I have two & I put one in the back bedroom where some of my cats like to hangout & sleep.
It's probably already chronic, that's why the vet suggest surgery. Yeah, 3k is to expensive. Did you try gov vet clinic? I think all district gov vet clinic can do surgery but I don't know whether they can do this surgery. Where do you live? Maybe you can try UPM vet hospital. I heard they charge reasonably.
BTW, if anyone want to neuter/spay their cats but have little budget, you guys can try check out your nearest district gov vet clinic. For example, Kerian (Parit Buntar, Perak) district gov vet clinic offer neuter & spay services for RM40 & RM80 respectively. I don't know about other places/states though.

I'm guessing you're using non-clumping litter? Depending on the environment where the litter box located, the non-clumping litter can get smelly quickly. If you have sensitive nose, better use clumping litter. The only non-clumping litter that best in controlling odor, IMO, is crystal type litter but you still need to replace it every week or two.

Also, if I'm correct you're using non-clumping litter, this could explains why your kitten relapse. Some cats very sensitive with the smell & refuse to use the litter box, even though the litter only a couple of days old.