[libc] Redo the install targets (#78795)

Prior to this change, we wouldn't build headers that aren't referenced
by other parts of the libc which would result in a build error during
installation. To address this, we make the header target a dependency of
the libc archive. Additionally, we also redo the install targets, moving
the install targets closer to build targets and simplifying the
hierarchy and generally matching what we do for other runtimes.