Hello: Its getting complicated-er! The odor should be the same from any tap. One thing that can affect things is the drain/overflow. Bath sinks have overflows which can smell awful as they never get cleaned. The stink is pushed from them when water is run. The kitchen sink though has no overflow, so should not smell worse.
Another variable is how far from your nose the odor is. Shower drains may seem to smell a little, but when you stick your nose down there, it can just about make you gag! If you have a way to sniff the water directly from the softener, before it gets to the heater, it might be nice to verify that there is no odor from that source.
It’s a little strange that softened water was tested for iron. I’d have checked for calcium hardness too, to see how well the unit was working. 🙂