Einstein derived the constancy of the speed of light from the Lorentz equations, called it "postulate", and finally derived the Lorentz equations from the "postulate":
John Norton: " The mathematical apparatus needed to complete this approach had already been developed by H. A. Lorentz in his theorem of corresponding states. Einstein knew well an earlier version of the theorem from Lorentz’s work of 1895. The difficulty of pursuing the approach is that a full implementation requires that more than field quantities transform in unexpected ways. Spaces and times must do so as well. Lorentz introduced an auxiliary time variable, his “local time,” in each inertial frame of reference. To complete the approach, Einstein would have to accept that this local time was just the time simpliciter of the inertial frame of reference. That would in turn require Einstein to accept the odd result that judgments of simultaneity would differ according to the frame of reference. Once Einstein accepted this result of the relativity of simultaneity, all his problems were solved. He could retain Maxwell’s equations unchanged and with them all their many experimental successes. He had no further need of the troublesome emission theory light. The speed of light would remain a universal constant c, the same value in each inertial frame and independent of the motion of the emitter. This conclusion would be elevated in Einstein’s 1905 paper to axiomatic status as the “light postulate.” "
Why didn't Poincaré come to the conclusion that the speed of light "would remain a universal constant c, the same value in each inertial frame"? Because that conclusion was nonsense. Both Einstein and Poincaré knew it was nonsense but the latter had conscience while the former hadn't:
John Stachel: "But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair."
Olivier Darrigol, The Mystery of the Einstein-Poincaré Connection: "It is clear from the context that Poincaré meant here to apply the postulate [of constancy of the speed of light] only in an ether-bound frame, in which case he could indeed state that it had been "accepted by everybody." In 1900 and in later writings he defined the apparent time of a moving observer in such a way that the velocity of light measured by this observer would be the same as if he were at rest (with respect to the ether). This does not mean, however, that he meant the postulate to apply in any inertial frame. From his point of view, the true velocity of light in a moving frame was not a constant but was given by the Galilean law of addition of velocities."