I was asked this on Discord, and here's an off the cuff lore answer for you (as always out of game answers are not technically "canon" but if I get a chance and it doesn't cause a conflict I'll try to stick it in a lore book):
It was the Staff of Office of the High Priest of Loarnab during the late First Age before Zaros's invasion. After Zaros conquered the area, he set up his own priesthood. While he had a few specific commandments (like "worship no other god but me"), he didn't provide any aesthetics or iconography for this new religion.
The human priests largely incorporated their existing cult practices. Zarosianism initially had no equivalent of a "high priest". A council of cardinals were responsible for divining Zaros's will, and the office of Pontifex Maximus was not created until later. Because Zaros was humanoid (unlike Loarnab) they could depict him as carrying the Staff of Office, which communicated his authority effectively.
The actual staff may have been preserved as a relic, or may have been lost during the conquest or at some later point in the long, chaotic history of the Empire and its fall. It's unlikely that Zaros ever held it or even knew of its existence, as such trivial cultural matters were of no interest to him.