how much of the water vapor remains a greenhouse gas and how much of the water vapor manifests itself as clouds?
That I don’t know, but a relevant factor to keep in mind about that is that more water can exist as vapor in a given volume the higher the temperature is. Given that, I would imagine we can expect a rise in global humidity (total water vapor content) accompanied by a smaller rise in global cloud cover as temperatures increase. The total amount of water condensed into clouds will increase, but the fraction of atmospheric water mass contained in clouds will be lower.
Another relevant question is whether a rise in global temperature would lead to a higher fraction of clouds forming at higher altitudes. If that happens, any cooling benefits provided by clouds reflecting incident light is erased by higher altitude clouds reflecting a higher percentage of infrared radiation from the Earth’s surface back to the ground than lower clouds do (because, as I understand it, once infrared escapes to the upper atmosphere, it encounters less water vapor per cubic meter, so the marginal difference a cloud makes is larger).