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.
From what I’ve read on this, hot-dry places will get hotter and drier, with intense desertification. Places that are typically wetter will have more frequent bouts of flooding and unusual rainfall patterns, like places that traditionally had "balmy’ weather might experience sudden 40day+ continuous heavy rainfall.
Also, even though on a whole the world average temperature will increase, cold weather will also tend towards the extremes with longer, colder periods.
Here you can see the effect of increasing global temperature on precipitation:


