What would happen if you kept adding water to the earth?
As a hypothetical, say it became easy to grab water from objects in space and then move it places that needed (Africa / the gulf). What would the end results be for the global climate over time? Would you just end up with a flooded earth? Would temperatures rise or fall as time goes on?
https://calculatedearth.com/ allows you to see what would be left above water at a given amount of sea level rise. It's not a complete answer to your question but you can use it to run animations with different ranges of added water depending on how crazy you want to get with your sci-fi scenario.
If it’s a small amount, I don’t think it will matter much.
If it’s a huge amount, it will become part of the water cycle systems. Oceans/seas/lakes evaporate surface water, which become clouds, which move around, then hit mountains and other things, get squeezed, release rain, which generally flows back to oceans via rivers. It may get stuck in lakes, or as snow on mountains, but in the big picture that is temporary.
Adding more water will likely put more in the oceans, as that is what holds most water right now.
Based on what I read about melting icebergs, If you add enough sweet water to oceans, it might mess with how water flows between oceans, which upsets how air flows across the planet, and thus it messes with large scale weather patterns. For example, Europe benefits massively from patterns that feed it warmer air.
Imagine Europe getting the same low amount of rain as the Sahara, or the Sahara suddenly getting the rain Europe gets right now. It’ll be a catastrophe if that persists for decades or longer.
For starters even if we could do that, I doubt the water would go to places that actually need it. Heck it's not like we don't have enough on Earth already, we already very much COULD supply poor African countries with the water and food they need, we just don't.
If we could drag resources from outer space, only the countries that are already rich would benefit.
How much are we talking here? If it's a shitfuckton I'm pretty sure it would get warmer as ice and land mass would get covered by less reflective water and more water vapor would accumulate in the atmosphere as a greenhouse gas. Also Kevin Costner would be out there doing his shenanigans trying to find some land so we just generally want to avoid this whole scenario because the man is too old for this shit at this point.
Within our solar system, these two moons carry a lot of water. Both very cool planetary objects, but not one of them is overflowing like in your imagined planet. We can't really study planets outside of our own neighborhood in high (enough?) detail yet, so this is it for now :P
Extrapolating a bit, what if we brought in enough water to cover the entire current exosphere? Or if you added enough water that the planet engulfed the moon? How would the water behave at those extreme pressures? What would happen to the landmasses beneath it?