It's exhalations really. Their BO would result mostly from bacteria that live on their surface. You exhale your metabolic byproduct of CO2, they exhale their O2. Just, instead of one centralized set of "lungs", their respiratory system is decentralized through the structure, kinda like a lobsters "brain" is. Kinda.
Plants "breathe" normally too, taking in oxygen, and producing CO2. Separately, they also take on CO2 and sunlight, and produce "food" and expel oxygen.
Since it's a by-product of their "eating"... It really is a fart, isn't it?
The main thing for me is that the contents of flatulence and BO were not made by the animal themselves. They were made by symbiotic bacteria.
Regarding plants taking in O2 and expelling CO2, to my knowledge this only happens at night, and the plant is not actually using the O2. It's just concentrations naturally equalizing while it waits for the sun to come back. Do some plants actually have a use for O2? That's out of my wheelhouse.
Anyways, I can see the flatulence argument, since both are a result of a "feeding" behavior, but there's not a lot else in common.
I guess, yea, they're making sugar, but they're still going to need to metabolize it. Why do I have the impression I probably knew this at one point in time...?