cooked egg back in the raw egg bowl?

If you are talking about strict food handling practices, yes- it would be cross contaminating the cooked end product. On the other hand, eggs tend to continue cooking, due to retained heat, for a short time after being removed from a pan. So it's entirely probable that whatever raw egg essence remained in the bowl would be "cooked" from that carryover heat. The way the recipe directs you to proceed though would not require you to put cooked egg back into the used bowl at all though. If you are concerned about your eggs and contamination, then you would naturally take precautions to avoid cross contamination.