This is assuming végétation does the majority, or all of the oxygen creation. I could be wrong.
Most free O2 in the atmosphere comes from photosynthesis in the ocean. So are you assuming the oceans are dead as well?
Even so, no cite, but I believe it would take a long time. Animal life would die pretty quickly without a food source so the major consumer of O2 would be oxidation of minerals.
Somewhere around 50% to 85% of oxygen production comes from plankton.
But allowing that all plant and plankton disappeared, I’m thinking that it would take geological timescales before the amount of oxygen was low enough that we would asphyxiate, but single-digit years before almost everything multicellular starved to death.
I once saw an estimate that it would be about half a million to a million years before the oxygen is gone from the atmosphere if it stopped being produced. Not because animals would be breathing it but because it would combine with rocks, especially new lava. Don’t remember where I read that or I’d give a cite.
There are about 10^18 kg of O2 in earth’s atmosphere.
A human uses 550 liters of oxygen a day. That works out to maybe 1.5kg a day (I think).
So a very very long time.
Carbon dioxide is actually toxic above certain levels; it’s just not normally present in that concentration in the air we breathe. I’ve read that if you cut a person off from an outside source of circulating air, the build up of carbon dioxide will kill them while there’s still a breathable amount of oxygen.
I’m guessing this would be a factor if plants disappeared. We wouldn’t die from a lack of oxygen being generated. We’d die from a lack of carbon dioxide being removed from the air.
Plants not only produce oxygen, they also consume it. Plants respire and use oxygen for their normal metabolism. There may be something like 500-1000 times more plant biomass than there is of animals. So if plants disappeared, this oxygen would be available for animals to breathe.
I agree that humans and animals would starve to death long before asphyxiation became a problem.
A more serious question - Would “recycling” humans/animals delay the starvation by some amount? Would we be missing some essential nutrients?