I've heard the fact wet air contains more oxygen is the reason experts recommend to humidify the air. Intuitively, I'd say wet air should contain water of a greater density and thus, make less space for other substances like oxygen. So (why) would wet air contain more oxygen?
Wet air does not contain more (free, molecular) oxygen, but can be subjectively more pleasant to breath than too dry air.
Wet air is effectively a mixture of dry air and water vapour, therefore content of nitrogen and oxygen is lower, if water vapour is added.
But the difference is effectively negligible.
If content of free oxygen is higher in wet air anyway, it is not because of air being wet.
It is because of other reasons, like due activity of plants, or if it is replacement of dry air with part of oxygen spent by breathing, with fresh, but wet air.