what she focused on (always, always--nothing about my biological mother) was that she was there to cut my cord. How... metaphorically on the nose, amiright?
You are, I am sad to say, spot on. It is incredibly cruel, in such circumstances, to deny you the right to your history pre-birth, pre adoption, and not to acknowledge it. Bizarrely cruel. I can't comprehend why your adoptive mother would say this. and avoid acknowledging the circumstances of your birth and your biological mother, your biological heritage.
In the past when the topic has popped up in general discussion with our own sons, my partner and I have told them about when we discovered they were expected, was it planned (no, both times..) what were doing with our lives at that time, where we lived worked etc. We also talk about the what it was like for their mum when she was pregnant with them, any particular experiences, and of course we tell them the story of their birth.
This is all pre-birth history, and although none of it is a planned conversation, I have come to appreciate it has enormous value in reinforcing the emotional and psychological bond between us and them. For me it throws into even greater contrast the experience of children separated from their biological mother at or soon after birth, (and probably for kids in other situations and circumstances too).