OK so, the interaction between temperature of the planet and moisture in the air is very complicated. This is because the air/water interaction is also dependent on where the air and water are.
Apparently, tropical temperatures have not risen as much as polar temps. The area of the tropics (within 23.4 degrees of the equator) is much larger than the polar regions. So, the evaporation into the air of tropical water is not going up that much.
But the real temperature changes are mostly in the boreal areas of the Earth. Antarctica, not so much. Equatorial, not so much. So, climate change is ill defined. Using the average temperature of the Earth as a metric to answer your question is not fecund.
Polar area is 8.25% of the Earth.
Tropical (torrid) area is 39.8% of the area of the Earth.
Temperate zones are 52% of the area of the Earth.
Again, temperature of the planet has change little in the tropics, some change in the temperate zone, and a lot in the polar regions. Water evaporates into air better when the air is hot. But even if ice leaves in the polar regions, the temperature is near freezing and the area is relatively small. So warming in the polar regions has only a small affect on atmospheric moisture.
But air masses from each region mix and moisture is exchanged between the tropics to the temperates to the polars… But that is way complicated. Modern computer modelers think they know. I doubt it. None of this can be tested. That is, you can’t raise the temperature of teh tropics, wait awhile and see what happens…then lower the temperature of the tropics and see what happens… repeat.
Climatologists will tell you that they can by using proxies to estimate the temperature record of the past. Tree rings, Tex86, Mg/Ca ratios and others are not the sort of science that brings you this computer that you are reading this entry with. I would never ride on an airplane designed by techniques used by climatologists. Climatology is very sophisticated, but poor science. Low on experiment and high on statistical modeling.
The water cycle of the Earth is a very powerful driver of the temperature of the planet. And the temperature of the planet is a driver of the moisture in the atmosphere. Feedback? Hell yes, and we don’t know the feedback parameters well at all. Oh, you want an example of complicated? What phase is the atmospheric water in versus height and latitude? Liquid, gas, or solid? Could be any of them.