The Mayor shall be the chief executive officer of the Municipality, charged with the duty and cloaked with the authority to supervise the administration of all departments and divisions of the Municipality, unless Council shall otherwise provide; except that he shall not have such powers with respect to the affairs of any department or division of the municipal administration which by this Charter is placed under the supervision and direction of a board which is chosen by popular election, nor as to an elected office holder, nor as to personnel holding office or employment in the municipal administration by virtue of being appointed thereto or employed therefor by direct and sole action of Council.