I agree.,..and I'm so sorry! Does look like a tumour and a very nasty one. Since it has been there for a while, it is certainly not an aggressive cancer ( like lymphoma which can appear practically overnight and kill very quickly), but cancer is the major cause of death in budgies.
From my understanding, and the times I've had to deal with tumours and birds, operating is not really a viable option. They are awfully small little creatures and the stress of the operation, let alone getting all the tumour, would most likely be too much for them. In addition, the tumour is probably not just on the surface, but goes into the body which means attempting to remove it could bring the doctor perilously close to major organs. In a bird, it's all so close.....
Obviously, take the little fellow to the vet and see their prognosis. I hope I am mistaken about all this.....it just looks too familiar.
