Perhaps "living API" analogous to "living document". Much more positive connotations ...
Perhaps, but that's pretty much coining a new term, which we would then have to explain. And since the opposite would be "dead API", what is a dead API exactly? And doesn't it follow that all APIs are living? If we stick with unstable, we're adopting a term that's in use by at least one other language community (Rust), and the slightly negative connotation is welcome -- people should think twice before using unstable APIs.