Yes, you need to get her to a Certified Herp/Reptile vet immediately, not a general vet or an exotics vet, but a reptile vet with Beardie experience. It does very much look like it's "necrotic" tissue, which means he has an infection that has caused the tissue to die. It will only continue to spread and go worrying about having his foot amputated, yes, you probably will have to have that done, but it might be the only thing that saves his life at this point. It's been over a week, and unfortunately if you don't get him to a Certified Herp Vet to get antibiotic injections along with oral antibiotics and possibly an amputation, the infection will quickly spread to his bloodstream, making him "septic", and once that happens he will surely die. So time is of the essence at this point for him, because if you let it go much longer you won't be able to save him.
Sorry for being so direct but I'm not going to pull punches with you, sea salt isn't going to help you, nor is anything else that you can buy without a vet. He needs prescription antibiotic injections, and like I said, probably that foot amputated. But he can live a quality life without a foot, I'm just afraid you've waited too long. Reptiles hide illness and pain as long as they can instinctively so if he suddenly becomes lethargic and stops eating that most likely means it's too late. Get him to a vet right now!
