What happened to the Master's blue laser powers and why doesn't (s)he have them in the Peter Capaldi episode with Missy?
The Master did not normally have such powers. As a Timelord, he has broadly the same abilities as The Doctor.
The "blue laser powers" you are referring to, as seen in the story 'The End of Time', were a result of a supernatural ritual meant to restore his life, but went wrong after it was sabotaged by Lucy Saxon. The life-force that he took from several humans, presumably meant to restore multiple lifetimes to him, was burning up much faster than it should have. When The Doctor saw a demonstration of these new abilities, he warned the Master that this would be to his detriment:
DOCTOR: Please, let me help. You're burning up your own life force.
Evidently, the "lasers" we see shooting from his arms, which he used as a weapon and also to enable him to fly, was his own life force.
At the end of the story, the Master disappeared along with the other Timelords back through the portal they had opened, thus returning to the time-locked Time War. It is later stated in The Doctor Falls that the Timelords "cured" him, evidently resurrecting him and giving him a new regeneration cycle just as they had previously done during the time war.