My theory in this regard is that CP0 did in fact not exist at the time of your pic, it was only CP1-8.
However, the massive incident at Enies Lobby would have been world-shaking news and thus investigations may have been made into the events regarding, revealing the existence of CP9 to the world at large or at least risking so. So I could see the World Government, in order to cover up CP9's activities and the secrets kept, may have re-structured CP9 into CP0, which WAS introduced to the world during the time-skip as a way of ensuring the public that the WG was stronger than ever following the Summit War with Whitebeard, as well as helping to cover up CP9. Restructuring CP9 into CP0 would also help explain why it shares so many members like Spandam, Lucci, and Kaku
Giving them specifically to the Celestial Dragons to work for them may have been a result of Luffy's attack on them on Sabaody as well, wanting to increase the security detail that accompanies Celestial Dragons to avoid such an incident happening again.
tl;dr CP0 replaced CP9 specifically because CP9 failed/was discovered, so they're trying it again but this time with a bit more of a public face.