I've only just read this, I am SO sorry for you ...and so angry about the vet care he got at that place! OMG! If a vet made this mistake they should be bending over backwards to help your poor kitty now! That's terrible :-(
I hope he takes the food syringed. I might consider offering something like chicken baby food on a spoon once he's had his pain meds and just see if he feels like licking something up. Realistically though, if you can't see into his mouth we can't know how BAD the injuries are there and then how long it will be before he even wants to use that. Just makes me tear up to think about it :-(
I am sure Koda knows that you are helping him, they are smart kitties and through all of Zari's illness she's ended up with a hatred of the vet hospital but we're bonded closer than ever. She completely understood that all that I did was for her,despite hating the meds I was forcing into her all the time and taking her to the vet for horrible procedures all the time.
Keep an eye on his hydration, he might need fluids as he heals if you can't syringe enough into him. And yes, the anesthesia and the pain meds will slow his gut so he may not poop too soon. I agree with Patti's suggestion of crystal litter if you are worried about his paws...although what he's used to if clean should be ok. Or you could try a puppy pee pad in a litterbox and see if he would accept that? Those things are scented so they know to pee there...
I hope his poor mouth heals fast. Please do find out what anesthesia caused this!