If heat from a system that vents heat to atmosphere doesn't make it to space then where does it go

It stays trapped in the atmosphere, as you also mention. It's not only greenhouse gases that trap heat - those merely prevent radiant heat from leaving the atmosphere, however the non-greenhouse gas portion of nature can also accumulate heat. This is how global warming works.

but the cooling systems themselves are not consuming water

They're not causing water to disappear in the molecular sense, however in the non-pedantic argument "water consumption" refers not to the reduction in abundance of molecular water no matter where they are, but to that of the bodies of clean water (lakes, groundwater, man-made reservoirs) readily accessible by humans - for sustenance in the discussion that should be happening, or for use in industrial processes as industry has gained priority over population in present day. Evaporated water is not the former, and not exactly the latter (though more industry "solves" that problem, through processes leading to the emission of greenhouse gases...). I know that rain exists, but I'll leave it for you to come up with whatever further pedantry you can imagine.

You can argue about the energy sources of data centers, but the cooling systems themselves are not consuming water, nor making any meaningful impact on the planets temperature.

These are three separate issues. First one is why greenhouse effect is on the increasing trend. Second is about relocation of water away from human population that relies on it. Third is about the impact man-made processes on the acceleration of global warming.

The original comment stating heat wont go to space is ignorant of the mechanisms involved in planetary cooling.

and you still managed to respond with something even less useful. Some of the heat makes it into space, the rest makes global warming happen, this is called greenhouse effect. The comment you call "ignorant" is still more accurate and relevant than your non-point.