What a shame! Do you know what caused the original allergy diagnosis when fostered? What size are the bald patches, and is the skin healthy or is it red or blistered.
Is he only taking the apoquel now? If the vet hasn’t got any history passed on, I would really want them to go back to square one. It may sound drastic, but cutting out Apoquel and reducing steroids if he’s still on them, would show the real picture. Has he had a general blood test?
Drugs can cause so many side effects. Vets vary a lot too, and never be too accepting of them. They can always discuss it with their partners.
Humans get odd bald patches too, in alopecia areata. Possible causes being auto- immune problems, or stress. Mostly it regrows. With dogs, the hair growth cycle is slow, so it can be months. I had a dog with severe auto immune problems , including losing blistered skin and the hair. She wore vests when out, but it healed and the fur took a year to recover. My point is that you are so right to query what’s going on, and stop the problem getting worse .
I hope Jasper is settled into his new home . I’ve got two rescue dogs, likewise other family members. One piece of advice. I overlooked first time, was in being too keen to take them to new places. They find it stressful. Walk them round their regular route for weeks, so they get confident in their new area.
Do let us know how you get on with the skin /hair problem.