A laryngectomy is something an ENT would generally perform. However, these surgeries can also involve pretty extensive reconstruction which often involves a plastic surgeon as well.
However, once you’ve had a laryngectomy, you cannot speak normally again, and can only breathe through a hole in your neck. You don’t have vocal cords and your lungs are not connected to your mouth/tongue/lips to allow you to speak. You can eventually be fitted with a device that allows you to speak, but your voice will not be “normal.” So if he was speaking in his own voice a few weeks later, and not breathing through a hole in his neck, he’s yet again telling blatant lies.
If I’m not mistaken, he had also said his “brain cancer” had “spread” to his throat, which just … doesn’t happen. It’s possible to have 2 different primary cancers in the same person, but they would be separate disease processes. And the whole “infected artificial kidney” thing … is purely science fiction.
ETA: a laryngectomy and a tracheostomy are different. A tracheostomy involves placing a tube into the windpipe, below the vocal cords, so that the person breathes through the tube rather than their nose/mouth, but all the normal structures are still there, so it’s possible for the tube to be taken out once the reason necessitating its placement has been addressed, and the person can breathe and speak normally afterward. With a laryngectomy, the voice box is surgically removed and the windpipe is no longer connected to the mouth and nose - the person can only breathe through a hole in their neck. What he was seemingly claiming to have had was the latter … something that is not readily reversible.