Coming into this late. I'm glad Hope is doing better. I think giving her improvement that you may have had some hypoglyemia issues. 4.5-5 wks old just can not regulate themselves that well. Blood sugar can drop very fast especially when under stress. ie change homes,routines etc. Sounds like you have her on a good kibble now. If she can chew it, it shoud be fine nutrient wise. If she is have trouble chewing you could grind it coursely, wet it for 5 mins before feeding or supplement with a meat baby food like beef,chicken or turkey, or puppy formula. Pups this young should be offered food every couple hours especially if active.
The vet probably put her on K/d as it is a kidney diet but also a low protein and if they thought she had a liver shunt. Low protein diet are part of the treatment.
Continued health to Hope.
Not trying to be mean but getting 3 month pup from a pet store is just as bad as getting a 5wk pup. Both are bad situations. Too bad it is the pups that suffer for it.

Both victims of breeder greed.