Currently, when copying and pasting classes that use Global Swatch colors between projects, Webflow simply converts the Global Swatch color into a 'normal' color value when pasting the class.
It could be nice to have Global Swatches pasted over as well.
There could potentially be a similar 'conflict resolution' behavior as is used with classes and interactions:
If Webflow introduced the idea of updating/replacing existing name matches in the destination site (like discussed for classes here: https://wishlist.webflow.com/ideas/WEBFLOW-I-1195), then we could do something similar to Global Swatches too if the colors didn't match but names did: choose between adding a new Global Swatch, updating the existing one with a matching name, or using the existing one as-is.