All grease is petroleum based, with the synthetics adding a synthetic component. The real differences are in the thickening agent, whether lithium, calcium, bentone, etc. Lithium is by far the most common, with the others reserved for very unusual applications. I’m pretty sure all lubes on bicycles are lithium based, and so no problem mixing.

That said, I would check the manufacturer specs as to grade and vis, and use something similar. Campy is too small a firm to produce their own grease. I’m sure they have a refinery blend it to their specs, or just buy something “off the shelf” that meets their specs and repackage it. But whatever you buy, it’s always best to disassemble, flush and clean everything, and then relube. If you don’t flush out all the old grease, there’s a chance the old has water or other contamination, and that will rust a bearing.