[08-15]

You may be confused. At least here in Germany, we (mostly) implement 2G: "Geimpft oder genesen." -- vaccinated or recovered. (Depending on context, "getestet", meaning tested negatively, is also fine.)

So no, "natural immunity" is not treated any differently from "artificial immunity", and it absolutely is about getting out of a pandemic without too many people dying. By the way, there is no difference. Immunity is immunity.