I guess at the beginning, OP had no reason not to trust the rescue that she says she's worked with for a while. She followed their advice but as they say - you don't know what you don't know.
However there are lots of really experienced posters on here who gave up their time and knowledge to help - and they were roundly shouted down and told they were wrong, that OP was doing everything right and that the lethargic kitten would be fine once it had settled.
Unfortunately, to those of us with more experience, it was obvious that that kitten should never have been sent home with OP. It's never normal for kittens to be lethargic and even a quick google will tell you that if your kitten is showing lethargy or lack of appetite then it's an emergency and they must see a vet as soon as possible. That's even more essential when the kitten in question is only 4-5 weeks old.
We said all this, multiple times, but no vet treatment was sought for two days. It's upsetting to know that OP had a kitten that was clearly failing to thrive yet wasn't doing the right thing to help it.
I don't think all of that is OP's fault - she was sent home with insufficient training and equipment, wasn't told the kittens were so young and didn't have enough experience - but that doesn't make it any less upsetting to read, especially when, despite continuing to help, you're still being told you're wrong.