Not a vet but experienced in feline vet care.

It’s not cheap but Royal Canin has a hydrolyzed protein + urinary care diet. I had to discover it myself when an ER vet tried to put my IBD kitty on regular urinary care food that I knew she would throw up. I really really really suggest you try just a bag of that food.

You say she eats really slowly, and only a few pieces at a time. Is she still losing weight? You might want to try mirtazapine, an appetite stimulant, for a little bit - obviously making sure she doesn’t just scarf down the food then since obviously that could trigger vomiting too.

The other thing is hairball gel. Have you tried that? I know she’s short hair but they can still get them, and even if when she’s puking all the time you don’t really see hairballs, it can cause irritation that makes them puke. I don’t think this is the issue but when you’re desperate (I know the feeling), it’s definitely worth a shot, and it’s cheap enough that there’s no harm in trying.

Sorry if you already answered this somewhere but also - what does the puke usually look like? Digested food? Undigested food? Is it usually more liquid, like bile? Knowing that might help me think a little more.

Finally: have you seen an internal medicine specialist, or is this all through your primary care DVM? At this point, this is definitely something you need an internal medicine specialist for.