Discretion Is a Skill
There is a kind of professional who always has a story. They know who said what, and they will tell you. They are pleasant company. They should never be trusted with anything important.
Discretion is often mistaken for a personality trait. It is not. It is a skill, and like any skill it is learned through practice and kept through habit. It means noticing when information is not yours to share. It means answering the question that was asked and stopping. It means accepting that "I can't discuss that" is a complete sentence.
Both the Army and the Foreign Service run on this. Information is handled on a need-to-know basis not because anyone enjoys secrecy, but because careless talk has consequences that land on other people.
The habit should extend to personal life as well: what gets posted, what gets shared, and where personal details end up. That is not paranoia. It is the same discipline, applied at home.