Wind.
You’re totally right that there isn’t much vegetation there for turning CO2 into O2, but there also aren’t many critters there turning O2 into CO2 there either; in the end it all sort of evens out that the breathable oxygen doesn’t get locally depleted before wind and diffusion can bring enough fresh air back in.
Actually, much more oxygen is generated by the ocean than anything else. But plants and trees do play an important part.
The easy answer is wind. The winds that circle the earth keep the oxygen flowing all around the earth and most areas have pretty much the same oxygen level.
You start getting less oxygen at higher altitudes, and that’s because oxygen settles closer to sea level vs other gasses.
At sea level, the air is approx 21% oxygen.
At 5500 meters it’s approx 10.5% oxygen.
At the summit of Everest (aproxx 8900 meters) its about 6% oxygen.
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