I have some experience to share here but the piggy I talk about we think actually had a problem with swallowing and her tooth issues were secondary to this - she struggled to swallow, so she ate less, so her teeth overgrew - and looking at the teeth this was the first thing the vet treated. The back ones were very slightly overgrown and there was a spur which was making a sore spot on the tongue so back teeth were treated.
Upper Respiratory Tract infection?
It
is possible when syringe feeding for a while that a piggy can inhale a bit of the food and develop a lung infection but if yours had a general anaesthetic for his dental operation it is also possible that a lung infection developed from then. My piggy had a GA for her dental and then had to be syringe fed - we ended up having to get antibiotics about 5 days later and I was blaming myself a lot, but the vet was very honest and said it could have been syringing but it also could have been from the op. The antibiotics worked, so either way she started to feel better.
Painkiller
Did you get a painkiller from the vet to give him after the operation? We were given 'metacam' to have twice a day for a week after as the mouth can be very sore.
Incisors overgrown?
If he has started to eat some vegetables and is showing improvement that is great but as you know it is important to eat the hay and grass to
keep the back teeth down and if he can't manage these or the hard vegetables you might think that there is still something wrong with his teeth... perhaps as well as the back teeth overgrowing the front teeth have also grown too long for him to be able to manipulate the food. This happened to my girl - she was still being syringed two weeks after the dental operation (as I said - we think the teeth weren't actually the problem but at this time we didn't know for sure). I noticed her trying to bite at a piece of wood and mentioned it to the vet when we went back... a new vet was also involved in the examination and between them they could not see any problem with the back teeth but the front incisors had by now grown so long that piggy could not close her mouth properly (this was why she had been trying to bite the wood) so they used a little instrument to 'burr' the front teeth (cut them short but not with a clipper - it was some tiny electric cutting tool). Now she did not have a GA because if they can do it without that it can be a very quick procedure (she was done in about 15 minutes) but my poor girl actually got trimmed a bit too short and she was sore again with a big fat bottom lip. It made me cry to see her looking so gummy, and she was frightened and angry as you might expect, but actually she managed very well with painkiller and the teeth start growing back immediately. Her chewing action was much better straight away so I could tell that the overgrown front teeth had prevented her chewing food properly with her back ones. Does your boy have over-long incisors now... even if he did not when he first went in for his op? There are pigs on the forum that are missing bottom incisors completely (their top ones have to be trimmed regularly!) and still eat on their own, so if these front teeth are too long they can prevent proper chewing but if they are too short for a while it does not prevent it.
Hard to get teeth right
Like
@Siikibam said above not every dental op is perfect and even good vets can maybe not have so much experience doing the back teeth. But the fact that he is trying to eat and managing some things is encouraging.
What would I do
I would personally return to the vets to ask for (1) metacam painkiller, (2) whether antibiotics are now needed for the raspy breathing, (3) to look at and maybe trim the front incisors if necessary. If the vet is quite convinced the teeth are fine you might think about whether there is any abscess at the root of the tooth which means pain as he bites... it might be worse with the hard veg. I don't know how you would identify this - maybe if you touch under his jaw does he flinch or squeak? Does he have bad breath or is it OK? But I have no personal experience of this and don't know whether antibiotics would treat such a thing or whether an operation is needed. But check 1, 2 and 3 first because all of these happened to us after the dental operation.
PS In case you wanted to know my lovely girl never ate anything on her own again - although she was hungry and sniffed and sniffed at the tasty things I offered she just did not take the food. Eventually other symptoms appeared - top lip flickering uncontrollably as I tried to syringe a little fluid, a 'choking' face with head twisting sideways as she tried to swallow her syringe food which she could only take a tiny bit at a time anyway. She never did drool like some pigs with dental problems do - she just stopped eating. We could only guess at why. Your boy sounds like he has improved and can still make a recovery. Be hopeful, return to the vet and let us know how you get on. All my very best wishes for little Muffin