In general, we haven’t found a need to add anything to the water for a couple of reasons 1) we normally have the system in use for 10 days or less during the fermentation cycle and 2) the water is cold, so less likely to grow bacteria.
However, if you are using it for a longer period or as a warming system you should use a product like Clearwater Blue typically used for Hot Tubs. This will keep any bacteria at bay and not affect the Stainless Steel in the system. You may find this under other brand names, but what you are looking for is a bacteria/algicide which uses copper ions.
Never use Chlorine or Bromine tablets as these are both Halogens which will cause the surface of the stainless to be damaged.