I think that there are parallels to be made but at least from my experience I do not feel "like a slave being adopted." Adopted children can be coerced or stolen from their families and then many are transported great distances to become the children of others, usually more powerful and accepted. I agree there's a commodification that occurs of children, that there is "natal alienation" from the first family, and frequently the first culture and the child's racial identity, that adopted people have a right to access their original birth certificates and other information about their first families.
I think that there's this strong desire to erase the kind of inequality that drives adoption, to prioritize the happy perfect new family created through adoption, to hide the bad outcomes. I think that these beliefs in the "fitness to be parents", the "deservingness" of the adoptive parents, the "rightness" of the adoptive family, and rescue narratives make adopted children more vulnerable to abuse.
I think that there's a possessiveness that we confer all parents over their children that we usually don't think about that becomes really evident in cases of adoption between unrelated people. I think children, adopted or unadopted, do a lot of emotional and symbolic labor for their parents.
I think that adopted people are often infantilized as the children they were when they were adopted, and that plays out in families and at the governmental level because there are many states that do not grant adopted adult people their rights to their original birth certificates.
But I also think that because adopted children grow up into adopted adults--who are typically treated in the world as adults with rights (such as marriage, property ownership, compensation for their labor) except perhaps the OBC, or citizenship if there naturalization paperwork wasn't filed, who have the power to make decisions about their futures, who are able to create their own families who possess a recognized humanity--that it is also an experience really different from slavery. If I met a stranger on the street without my family and didn't choose to mention the fact that I was adopted, they wouldn't know.
So I think that there are many strands (commodification, natal alienation, often unrecognized diaspora, often unrecognized trauma) that are similar and confusing but they are ultimately distinct experiences/feelings at least for myself.