Buttigieg worked with McKinsey & Company, a management company who had a contract with the CIA. He may never worked on anything for the CIA at all, and has signed a NDA which he has kept. Accusing him of being a "C.I.A. spy!" is the least effective way to go after him.
McKinsey & Company is a known CIA front company.
They even worked with Brennan in 2015 to revamp the CIA management.
The top management of Burisma was former McKinsey.