> when did the term come to popular usage? When was it “invented”?

Its always been somewhat less popular than “biological parents”, but its been in wide use since somewhere about the late 1970s, and it (or at least, the narrower form “birth mother”) was in use by the early 1950s at the latest.

The reason why it’s qualified by people who are adopted is because people who aren’t would just refer to them as “parents” not “birth parents” since there is no need to make a distinction.

People who are adopted have two sets of parents so it’s used to distinguish who they are referring to.