Poop isn't CO2. It does have carbon locked in it but it has to be broken down to be useful.
CO2 is usable without processing.
I think you have that backwards ... the carbon in CO
2 is said to be fully oxidized, see the two oxygens? ... that is it's lowest energy state at environmental temperatures ... poopy carbon is bonded to other carbons, hydrogen, some nitrogen, oxygen and sulfur, few other things ... this carbon is said to be reduced, which is a higher energy state ...
Reduced carbon is a precious resource ... 3rd Law of Thermodynamics predicts this higher energy carbon will seek it's oxidized state and lower energy ... and a pile of poop is chuck full of reduced carbon ... we can smell it ... what atmospheric oxygen don't get, the bacteria will ... a pile of poop is a seething mass of microbes ... "One man gathers what another man [poops]" ...
Oxidized carbon must first pass through the photosynthesis pathway ... CO
2 + sunlight --> reduced carbon + O
2 ... only then is it vital and can be joined to other carbon atoms into proteins ...
Carbon is poop is already unlocked and available for use ... it is CO
2 that must be processed to be usable ...
( ... and you don't know shit ... )