Aziriphale, I've said it before and I'll say it again -- you have a gift for starting hot topics.
I am not an adoptee. And I am not a therapist or trained in the field of adoption studies.
But I am an adoptive parent who has done an enormous amount of research in this area.
1. My daughter is one of Mochi's "sweet little baby girls" from China. I won't say a lot about that, except that as a parent, it is extremely clear to me that adoptees can suffer from their abandonment or relinquishment and/or their months in orphanage or foster care. They may also suffer from the stress their biological mothers experience (and/ or the malnutrition) while they are in the womb. Babies may not "remember" consciously, but as Bessel van der Kolk says, "the body keeps the score." And trauma has long, long tentacles.
True -- in our situation it is difficult to know whether trauma or genetic inheritance or some combination are to blame for the challenges our daughter faces -- because we do not know anything about our daughter's birth family. (This is due to the probable situation that led to her relinquishment -- One Child Policy). Add to that the stresses (very real, even today) of growing up Asian in a Caucasion family. If that won't make you feel different, I don't know what will! Put it all together and she is dealing with an unusually tough legacy. As her parents, so are we. This is not "normal parenting" -- if there is such a thing in the first place.
2. The feelings you described are normal. It is very, very common for adoptees to feel "alien" in their families -- even if they love their families and have superb relationships with them. And, you are right -- this experience is of a different kind and order than that of the biological child who never feels "at home" in her birth family.
I was one of those children. I still don't feel "at home" or "understood" within my family. I love them, and they love me, but they've never really "seen" me. Not their fault. It's just not in them. This is common for kids with artistic temperaments, full stop. (So, in your case, adoption may have compounded a tendency that might have already have been there.)
Regardless, your feelings are real and are on a different order from what kids in bio families feel.
3. As an adoptive parent, I would not (and do not) feel at all threatened by the idea of my child seeking her birth family. Many adopted children worry they might be hurting their families somehow if they initiate a search. But it shouldn't hurt the family -- and if it does, the family should "suck it up." In this case, the adoptee's needs should take precedence. Full stop.
4. It is also normal not to want the information. I'm close friends with a man who was adopted. Both his sisters were also adopted. When it came to their birth families, they took three different routes.
Sister 1 did the search and find -- and was terribly disappointed. Bad result all round. But...to be fair...Sister 1 is not an emotionally stable person to start. Sister 2 waffled for a while. Eventually she did the search and had a reasonably good result. She didn't love her birth family but she saw what she needed to see and maintains a decent if cool relationship with them.
My friend (the oldest and the boy in the family) didn't want to do anything. My family's my family, said he. It's not that he had a great relationship with his adoptive parents -- it was pretty fraught, to tell the truth. But he did identify with them on some level and just wasn't interested in the bio family.
Then he had a medical emergency and his wife (a doctor) insisted that he ask for the medical records, at least, for the sake of their two biological sons. He did so, and was very glad to have these records. So were his kids. (They were tweens at the time).
5. A person can feel as close or closer to an adoptive child as to a biological child. For all her differences from us (and they are many) our daughter shares some passions and predilections that I'm not sure a biological child could ever share to such a strong degree. This goes way beyond the cute ways that adopted kids come to mimic their adoptive parents and right to the core. So...for instance, in our case -- our daughter often feels like an alien due to not looking like us, having different abilities, etc. And yet, she is also an artist and lives in a family that "gets" that. How amazing is that?
In other words, this stuff is incredibly complicated and interesting.
Oh -- another point -- she is rather young to make this decision, but she is hoping to adopt herself when she is older. So there's another possible counter-example to your argument about adoption following adoption. I actually know quite a few adoptive and foster parents who were adopted themselves and have chosen this role explicitly because they feel they understand the emotional issues that adoptees and foster kids face.
6. Mochi is dead on. Adoption agencies (and other institutions involved with adoption) lie lie lie. Not everything you see on the papers will necessarily be true. Sometimes it will be. A lot depends on context. But you can't necessarily believe it.
Phew. This got long, and didn't answer your original question.
Would I want my medical records/ birth certificate if I were adopted? Would I search?
YES. I would.
Having grown up in a medical family, I understand the value and importance of medical records, if they can be had. I would get every bit of information possible to pass along to my children (esp. biological children, if I had any).
Having said that, I don't know if I would necessarily search to the limits of the earth or to the ends of my resources. I would search until I reached a place of personal satisfaction. I would know when I had reached that place. It might be once I found and established a relationship with the birth parents. Or, then again, it might be until I saw the records themselves. Who is to say.
I would also give myself permission to go in stages. Maybe the records are enough for one year. Maybe the other need will come later. And that's okay.
And before I searched, I would seek some counselling and support to help me understand what I was hoping to find, how to manage my own expectations, how to buttress myself with the support I would probably need. i'd wait until I was feeling strong and ready for this, and I would try to look on it as an adventure in self-knowledge.
ETA: And in case it is not clear, I love my daughter with all the passion (and then some) that I would feel for any biological child and feel incredibly deeply connected to her. I love my step-kids in a similar way (though not as intensely as I did not raise them.) So-- biology is definitely not the fundament of love. Or a sense of connection.