Yes, there is any sense, then, in which Einstein’s second postulate can be viewed as contained within the scope of his first postulate.
In accordance to Einstein’s first postulate of special theory of relativity, the fundamental laws of physics have the same form for all inertial reference frames. But according to second postulate, the speed of light in free space has the same value c in all inertial reference frames that signifies that the velocity of light in vacuum is independent of the relative motion of the source and the observer.
The first postulate is the extension of the conclusion drawn from Newtonian mechanics; since velocity is not absolute, but relative which is a fact drawn from the failure of the experiments to determine the velocity of earth relative to ether.
We know that the speed of light is not constant under Galilean transformations and the first postulate is the conclusion from Newtonian mechanics; thus second postulate is not true according to Galilean transformations. Actually this is true since the velocity of light calculated by any mean is a constant. Thus the speed postulate is very important and only this postulate is responsible to differentiate the classical theory of relativity. According to Einstein, the theory of relativity is applicable to laws of optics. That is why Einstein’s second postulate can be viewed as contained within the scope of his first postulate.