It’s a wholly separate city from St. Louis - unlike many cities, St. Louis is limited by permanently fixed boundaries, it cannot incorporate more and more territory at will and expand its tax base. So no, it has not absorbed Ferguson, and Ferguson is no more “St. Louis” than East St. Louis, IL or Arnold, MO is, it has its own Mayor, etc. Contrast that with St. Louis’s Italian neighborhood, The Hill- that is a physical part of St. Louis.
Om the other hand, if you grew up listening to KMOX radio to hear the Cards you have a tendency to think you are St. Louisan even if you live many miles away from its boundary.
St. Louis is just the leaf-shaped area with the black line around it. Everything outside of that is a different political entity.