However, if I create my RenderWindow using the ContextSettings, and I set DepthBits to some reasonable value, I would expect Clear() to clear it, too.
That wouldn't be a good idea. You control what's written in the depth-buffer, you control its activation/deactivation, you control the clear value, so... you control the moment you want to clear it too.
SFML, on the other hand, doesn't even know what a depth-buffer is (except in ContextSettings, which makes sense only for external OpenGL code anyway).