Gold is not counted toward your wealth unless it is in a Designated Stockpile Zone. If it is elsewhere on the ground it does not count towards your wealth.
For example I had a stockpile zone that had all of the gold in it. I wanted to move the gold so I made a new stockpile for only Wealthy items. I removed the wealthy items from the original stock pile. They say there until they Hearthlings decided to move them to the new designated stockpile. I had a trader come and it showed 0 gold because none of it was moved yet. Then a daily update happened and showed I only had 200 gold. I looked at the new stockpile and sure enough there was 2 gold piles there.
I think that’s clear. If you need more information please let me know.