If Cookies seems otherwise healthy, it could be a tooth root issue. I’m surprised the vet didn’t suggest an x-ray.

Pardon the stupid question, but was this a rabbit vet you took Cookie to? Or was this a canine/ feline vet? I would take Cookie to get a second opinion from a different rabbit vet. One time I saw 2 doctors for a health issue (for me), and they sent me away with no solution. I even had an MRI, and it said I was fine. But I knew something was wrong, so I went to see a specialist, and sure enough, everyone had missed the problem, which had become worse with time, and which I had an emergency procedure for. Trust your gut. Go get a second opinion.

I agree, different vet. If possible, take some video of when he is making this noise while breathing. And photos of discharge if it’s not present while you are at the vet.
You might like to try a nebulising box using just saline to help him clear the discharge away. You could either hire a nebuliser or buy a small one. The boxes are just a plastic tote with lid that you place the bunny in, then put the nozzle of nebuliser in a small hole cut in the side. 10-15 minutes would be enough to help loosen the gunk.
brb, will try find video of this set up.

ETA: Heres a VIDEO.  Many people report their snuffly rabbits enjoy this after they become used to it. I’ve also read of people just holding their rabbit on their lap and holding neb mask just in front of the face helps also. 

Oh wow, I am asthmatic with a nebuliser and I had no idea that they did this sort of thing for bunnies. Good to know!

It’s really great for rabbits with chronic resp probs. Meds can be administered for rabbits this way too. It’s thought that when its a bacterial infection, the bacteria can stay trapped in the sticky mucous in pokects in the nasal tract. So an antibiotic may help initially but if any remaining bacteria is harbouring in these spots, the infection comes back after the course of abx is finished. So getting everything to flow out helps.

I picked up a baby room thingy (what are they called? lol ) that Im going to trial for Gooseman, who gets a bit snuffly. Most of these would probably not be suitable but Im hopeful the design of this one will work. Steamy bathrooms can help also!

Usually, the way to get a good look at the back teeth, involves anesthetizing the rabbit. It sounds like Cookie needs an x-ray of his mouth area, and an x-ray of his chest, since the croaking sounds are coming from there. Also, if he has any discharge, a swab should be taken of that and analyzed to see if it contains bacteria and what kind it is. I hope that you can get some answers and a good treatment for Cookie. If no bacteria is present, then it seems likely that Cookie has allergies. The allergies could be to certain hays or bedding or just allergens floating in the air. Rabbits can take Benadryl or maybe some other allergy medications if warranted. Hopefully, you can get a definitive diagnosis and be able to help Cookie.