How bad can symptoms be from a new diet??

New food causing stomach issues? How severe can it be?

Hello, we were fostering a 2 yr old intact male for a few days last week. He is so sweet and seemed immediately comfortable in our home. We kept him in the guest room with the door closed because we have a resident cat and wanted them separate for a while. Foster cat LOVED food the first few days. The shelter didn’t send us home with food so we figured we’d just give him what we have at home for our resident cat, tiki cat wet food pate and Farmina N&D dry food. He would gobble it down with such excitement and speed every time until around day 4-5 of him being here- he didn’t even touch his food. He was also resting a lot more but I attributed that to him getting more comfortable. Well fast forward to that night, he is throwing up several times. I slept in the same room as him to monitor him and he threw up in the morning mostly bile I assume because it was all liquid, but as I wiped it up and checked the paper towel it was slightly red indicating the presence of blood. I immediately called the foster coordinator and we promptly took him back to the shelter to be monitored 24/7 by their vet staff. It’s been 4 days since dropping him off and the shelter says he hasn’t vomited once and is getting much much better- eating and drinking and pooping like normal. They called and we were trying to eliminate potential causes of this stomach irritation / blood in vomit. Their first thought was a foreign body but I made sure his room was entirely cat proof because I am extremely cautious about that (due to anxiety and OCD). I already do this with our resident cat too because I have always been terrified of him ingesting something harmful. So to be honest I think the chances of foreign body are slim. The foster coordinator suggested maybe the new food was causing this- but in my head I’m thinking new diet would also cause diarrhea but he’s had normal healthy poops this whole time. And would a completely new diet cause bloody vomit? I didn’t know it could be that severe? Can anyone help me eliminate causes of this? I’m worried for two reasons- 1) if it was a foreign body what if he gets into whatever that was again when he comes back (despite me sweeping the room floor to ceiling for potential risks and for any proof of ingesting an object or anything) and 2) if it was a foreign body would he have health problems down the road if it’s still in his system? Despite him showing signs of improvement?

TLDR: foster cat on completely new diet vomited blood after 4 days of tolerating new diet perfectly fine. Unsure if new diet was the cause of vomiting / blood but trying to eliminate possibilities. He is doing okay now!