"Dans sa poche au chat" is not directly related to the art of speaking nothing. It is a common expression meaning "to keep something secret" or "to hide something", suggesting someone is keeping information close to their chest.
While "dans sa poche au chat" can be used to describe a politician who is not transparent about their intentions, it's not the primary expression for describing the art of speaking nothing.
"La langue de bois" is the most common and accurate phrase to describe this political tactic.