Water evaporates constantly in from soil, plants, and water bodies - most notably from the ocean itself, which is how ~babby~ precipitation is formed. Evaporation from a datacenter is unlikely to make any notable impact through water vapor. What it could impact is highly localized potable water availability and humidity in places with e.g. low precipitation and limited reservoir capacity.

And, again, note that other cooling methods are also in use, and that other things also use evaporative cooling.

Heck, even when evaporative cooling is used, it doesn't necessarily mean that the water escapes into the atmosphere! Both heat pipes and refrigeration cycles are forms of evaporative cooling where the gas is allowed to condense, cool and evaporate again.