Has anyone had experience with high protein low carb diets in older dogs?

We have a 13 yr old pug that has some eye discharge that he rubs off with his leg and licks that leg constantly. We were told that is very likely because there are too many carbs in his diet and it was recommended that we put him on a high protein low carb diet, more of a keto diet similar to what they'd eat in the wild. Clearly, a Pug is about as far away as you can get from a wolf and I have to assume that after several hundred generations, the need for a "wild" diet has been bred out of them. No one seems to agree on that however. We are careful with his food intake and watch his weight. He's currently and for several years been eating a grain free Salmon/Potato kibble. The problem is, at least from the foods I've checked, the amount of carbs is not listed. His current food is 25% protein and 14% fat. A Keto diet would have significantly higher protein and fat I assume. I know there are a few Vets and Vet assistants that frequent this Reddit, perhaps you, or anyone else familiar with this issue could answer this ? So far, with people I've asked, no one seems to agree. There is a far larger audience here.