At this point I'm not really suspecting toxic exposure because that typically has an effect on all of the limbs, causes uncoordinated movement and depression. I'm glad the wounded limb is healing.
The anorexia from a tooth spur can certainly account for just about any kind of infection, especially infection in the mouth. Urinary tract infections in chinchillas are not too uncommon and certainly can be caused by a compromised immune system from malnutrition.
The foreign object could be a number of things, even an artefact on the x-ray that isn't really there but you do have a lot of things going on. If you get another x-ray you can compare them to rule out a misdiagnosis.
My recommendation is stop feeding treats altogether today. Treats can actually cause irritation to the digestive system and make the problem worse. Compensate with critical care over the next couple of days if needed but I'm hoping that's going to spur better eating habits and it can take a few days before your pet gets used to the idea there are no more treats. Make sure there is loose hay and regular pellets in the cage at all times. I think 20g fluctuations in a 570g chinchilla is abnormal but not extreme. The big question is going to be what is its healthy weight that you're trying to maintain.
Chinchillas are very good at hiding illness. Usually by the time they develop symptoms it's really bad. My advice is try a sensible approach to get him off the critical care and discuss a strategy to do this with your vet. This will require weighing, monitoring fecal output, etc. and setting limits that you don't want to cross if the process doesn't work. If there's no improvement in a week your last resort is to have the teeth looked at again. It's not uncommon for spurs to get missed.
I hate recommending euthanasia for any pet but I think you need to think it through and set limits on when it might need to be done and how far you want to go ahead of time. Dental malocclusion is a terminal disease and sometimes it is just going to be this way for the rest of the life of the animal. I know of owners who have hand fed their pets for months, get filings done every month or so for years and they'll go through ups and downs until it gets bad enough that treatment is no longer an option. Although results will vary depending on the severity of the problem.
Malocclusion is usually caused by improper breeding practices and inadequate pre-natal nutrition. Sadly, many breeders make little or no effort to keep maloccluders out of the line. If you've obtained your chinchilla from a reputable breeder they will be interested in the x-rays and results.