When we were looking at adopting a child, I read a lot about adoption. I was very discouraged by what I read about the inequalities and abuses of international adoption. So domestically, there was adopting from "the system" (the state) or private. We have a very very good Open Adoption (private, non-profit) agency here (which costs $$$$ for the adoptive parents despite being a non-profit).
An Open Adoption means ongoing contact between the birth and adoptive families. To enter the adoption, we would receive intense counseling about adoption and attachment, do all the required home studies/inspections, and set up our parenting profile, and then wait to be chosen by birth parents, who are also given a ton of counseling. (The agency wants the birth parents as informed as possible, and more counseling = the less likely they are to change their mind during the process.) The bio and adoptive parents set up an agreement (it is a legal contract) for how often the adopted child will see the bio parents.
It is a very intense process and the losses inherent in adoption are recognized. We decided not to pursue it, that is, to not be parents, but I think it is the best adoption process I could imagine. Our good friends did pursue it and were chosen as parents two years after they entered "the pool". They had to decide whether the birth family was a good match for them, which was actually a difficult and time-sensitive decision, and they chose to go forward. They were present at their baby's birth.
I think their legal agreement is 3 visits a year with the birth parents (until the child is 18), but they have had more contact than that with the birth mother (and her mother) in the first year, and lots of sending photos. She sends the baby knitted things.
I wanted to add this to the discussion because adoption has changed, so much and recently. Open adoption would have been unheard of in the 60s, and been considered bad or confusing for the child. It doesn't answer Aziraphale's original question but it won't be a question for him. He will grow up knowing why he was adopted and knowing his birth family as an extended family.