Cat losing weight with unknown diagnosis

My 12 year old long hair tabby has been losing weight rapidly the last few weeks. At her youth and healthiest, she was 12 lbs give or take. At some point she went down to 9lbs and labs only showed a UTI, not any kind of kidney disease or diabetes. This was about 5-7 years ago.

Fast forward to two weeks ago and she was 5.6 lbs. last week she was 4.8. She is skin and bones. At the clinic, the vet did not notice any lumps, teeth problems, or anything that would cause concern when examining her.

All her labs came back normal, so the vet thinks it could be something sinister like cancer that may be hard to detect, or possibly IBD. She was prescribed prednisone and an appetite stimulant, with mixed results. She also had an antibiotic and fluids.

Occasionally she will devour her wet food, and other times she’ll go a day or two without eating or barely eating. She doesn’t touch her dry food. This behavior has been going on for weeks. I’ve noticed her slowly losing weight over the years and she’s never been a big eater. She currently asks for food, but doesn’t eat it, not even her treats. Sometimes she’ll take a couple of her treats, but it’s very inconsistent. She seems her normal self, very affectionate and not seemingly in pain.

I’m not sure what to do at this point. I’m not willing to spend thousands (I’ve already spent close to $1,000 in the past couple weeks). The vet and I have discussed putting her down.

Another thing to add is we have a newborn in the house and a lot of this behavior happened shortly after she was born. I missed the subtle signs in the beginning due to just being very distracted with lack of sleep and another toddler in the house as well.