While I’m thinking about it, I have a question for you on a different subject.
In your opinion, is a stepchild still called a stepchild after the stepfather adopts the child?
No. Not appropriately anyway.
Referring to an adopted child as a "step child" would constantly remind the child in a painful way that he really isn't considered as a "real" son or daughter, but is rather an "artificial" son or daughter.
If someone wants to perpetuate a distinction, they should not adopt the child in the first place.
Now if others do it, it cannot be helped, but under no circumstances should the father or mother do it. (and they should advise others to desist.)