What should this person do about the sins for which he has not repented, and about the blasphemous thoughts that constantly trouble him during worship, and which were not present before his repentance?

Praise be to Allah who has accepted the repentance of this person. And let him know that his repentance will not be accepted unless he regrets the negligence and shortcomings he committed regarding Allah's rights. These whispers are from the plot of Satan, so he should not pay attention to them or give them any importance. And let him know that they do not affect his faith as long as he dislikes them and is repulsed by them. Indeed, his dislike for them and his repulsion from them are signs of the sincerity of his faith.