There is no salt as such in the softened water provided by a water softener, as salt is generally accepted as being "Sodium Chloride" and as all chlorides are removed during the water softener regeneration process, only a fine (trace) level of sodium remains.
As water softeners do not allow chloride into the softened water supply and work on the sodium/calcium ion exchange principle, chloride is not the ion exchanged, and is sent to waste, and is therefore barely found in low single figures in softened water of 1 or 2 ppm where 250 ppm is the safe EU / HSE limit.
Chloride is effectively the salty tasting ion from the two types of ion produced when dissolving salt (sodium ion and chloride ion). Salty taste requires a far higher level of chloride ions when found in solution with metal ions like sodium, calcium, potassium etc. Chloride is key to the salinity in all cases.
The Mayo Clinic website is the leading global medical website with the most PHd qualified staff world wide contracted to post articles and gives a very good account of softened water and the definition of very low sodium.
The only level of sodium left in softened water is around 80 ppm to 160 ppm when hard waters from 200ppm to 400 ppm are softened. The EU / HSE limits for sodium are 200 ppm which many bottled waters, fizzy pop, milk, other beverages, which are less regulated, exceed.
Bottled waters like Tesco Still and San Pellegrino have 90 ppm to 135 ppm of sodium plus the saltier tasting chloride at another 50% above the respective sodium levels. Supermarket milk has 300 to 500 ppm of sodium, and again another 50% above these figures for the saltier chloride ions.
As sodium chloride salt in total can only be tasted by most people at levels dissolved in water from the 1,000 to 3,000 ppm level up to 15,000 ppm in some condiments like soya sauce, it is very hard except for the super sensitive to taste or sense trace levels of the "salty" chloride in water at around the 100 ppm level as with the likes of bottled waters.
Softened water of course does not have chloride so is not salty tasting, especially as sodium is also fractional at just over 100 ppm on average.
From the HighBloodPressureMed.com site ...
"Soft water contains all of the biological mineral deposits that we tend to require. It is only deprived off its calcium and magnesium content, and sodium is added in the course of the softening process. That is why in most cases, softened water is absolutely protected to drink. It is recommended that soft water accommodates only up to 300mg/L of sodium."
In many Asian countries, sodium as part of mono sodium glutamate in much of the cooking often exceeds 1000's of ppm in the average diets, - the more questionable chloride is not seen in these levels, yet heart related conditions are very low in these countries.
Lo-salt supplementary table salts and reduced sodium salts have potassium chloride as the main ingredient, and are as salty tasting because of the chloride content.
Water softeners are classed as very efficient appliances for total water use for backwashing and rarely use more than 4% of total annual water supply if correctly sized, installed and calibrated.
Metered systems are the most efficient currently available, and the least hungry for salt for their regeneration cycle, usually 3 to 6 bags of salt per year - 20 to 40 euros per year.
Toilets use around 30% of all household water use, and leaking toilets with sticky ballcocks can easily lose up to 3,000 litres of water per day (per toilet) where the average total household use for water for all uses is from 250 litres per day.
So water softeners are frugal on water (unless badly sized, calibrated, installed), - toilets can use massive amounts. The worst water softeners are time controlled, small, or undersized systems, that have too frequent a wash cycle.
A water softener has a negative carbon footprint close to removing an average family saloon car off the road for each year a water softener is in use, for reductions of things like heating losses in water heating systems ...
Google the Battelle Memorial Institute Study.
For over 100 years water softening by ion exchange has been the only cost effective and practical method for removing hardness from water, - calcium and magnesium carbonates / bicarbonates, and as they have gained efficiencies decade after decade for lower salt use, always keeping within EU and HSE drinking water limits for sodium / chloride etc, they are as good as it gets for low cost household water softening costing around 30 euros a year when metered.