Voldemort didn’t put his soul into Harry.....his soul was so unstable that it fractured when the curse rebounded against him, and it attached himself to the only living thing in the house....Harry. It wasn’t intentional.
And when the final curse rebounded on him, there was nothing left of his soul to survive, since all the horcruxes had been destroyed, including that part of his soul he killed when he ‘killed’ Harry in the forest.