The hot water won’t contaminate the cold water. The mechanics of this phenomenon are that otherwise harmless bacteria in the water react with sulfur in the water and sacrificial anodes in the water heater to produce hydrogen sulfide gas.
I’m thinking you should consider an aluminum/zinc anode. Usually those work when no softener is involved, they’re cheaper than the powered anode, they last a long time, and they don’t require power to work. Also, once the anode starts functioning, there isn’t much to go wrong.
Get SKU11 if you have 44 inches of overhead clearance, or SKU12 if you have less than that, but at least 12 inches. I found that model in State’s spec sheets and it appears to have a hex anode.