I expect plant construction (especially lots of concrete) is a much bigger emission concern than mining the fuel (a little fuel goes a long way, although it takes a fair amount of mining and refining to get that little bit of fuel). The further down the stack you go, NOTHING is absolutely carbon-neutral (solar and wind construction require raw materials too, as does all distribution no matter the generation source), but it's a matter of scale vs. return.
At this point, it's not clear that the construction emissions of big nuclear makes it a net win over its expected lifetime when compared to solar/wind. And small nuclear is still mostly vapor, and not clear that it's actually solved the scaling costs that made huge nuclear attractive in the first place. Continuing to operate the nuclear that's already been constructed for a long time probably makes it a reasonable win (of course, if we ever get a more reasonable way to deal with the waste).
As for the water... big plants are typically built directly at water sources and manage it directly, so they aren't really "consuming" it in the way datacenters do (where they just want to hook up to municipal water sources and outsource the management costs). Plants are restricted in output water temperature so as not to cause harm to animal/plant life downstream, and while some (depending on design) do evaporate a bunch, it's still right there where it came from. So I don't _think_ they have a significant impact in the way datacenters do.