Afaik weather will become more extreme, so some regions will get very wet (flooding damage) (as we see currently with Portugal), and some very dry (drought).
From a physical viewpoint, climate change will heat up the oceans, so more energy will be available to lift up water into the atmosphere/clouds?
Yes and no, sometimes one after the other. Climate change is more about the climate destabilizing and becoming more erratic as opposed to moving in any particular direction.