I had a bird with Marek's that had a couple of subcutaneous tumours. It is not the norm, but with Marek's there seldom is any norm..... just some quite classic symptoms which may occur (or may not) and can point you towards the diagnosis and lots of spurious ones that could be anything or nothing. This particular bird of mine had a tumour on the thigh and the other just below the rib cage. I was not aware of them until I did a post mortem exam as she had other classic symptoms of paralysis. The substance of them looked a lot like that but they were not so pronounced and when you cut into them it was quite firm and looked like a mixture of scrambled egg and sausage meat.
I'm not saying this is Marek's but I think your initial assessment of it being a tumour is probably correct with that large blood supply. I appreciate that this is on her breast, but what does the other side feel like? Is she reasonably well padded or does she feel a bit scrawny. If it is a tumour, it will probably cause her to waste away as it grows. I'm not sure there is much to be gained by cutting into it, but then that is because I think it probably is a tumour..... if I thought it was an abscess then my opinion might be different, although with such a large blood supply, there is a good chance that the infection could be released into the blood stream by surgical intervention whereas it would appear to be contained at the moment since she looks quite bright and healthy. Unfortunately that healthy look does not rule out Marek's either as often they are bright eyed and red combed in the initial phases.
If she is a favourite pet then you might be wise to seek veterinary assistance but personally I would be reluctant to cut into it and would just keep a close eye on it... perhaps monitor growth and her weight and appetite (and poop) and give her as happy a life as you can but be prepared to euthanize if she starts to decline.
