These looked accordingly on the inside...
Made of what material? What does "accordingly" mean?
My neighbor apparently has a water softening system
Then he got involved with a good salesman (=scammer). With that hardness range, softening, as has already explained, is not a sensible investment.
3. I have a rain shower in the bathroom, which regularly gets limescale deposits
Evaporating water almost always leaves residues. It does not necessarily have anything to do with hardness-forming substances (Ca, Mg).
But if you say you can’t get below 7°dH anyway, then the effort and costs are naturally questionable!
If you want, you can get down to 0° with Lake Constance water, as there is hardly any sodium in the raw water. However, this is not sensible because hardness buffers the pH. pH changes can then in turn lead to corrosion problems, which you should hardly have anymore with current materials + Lake Constance water.
but my idea is the reduction of nitrate as well as the enrichment of minerals
Why? You have Lake Constance water, hardly any hardness, hardly any nitrate, hardly any sodium, top actually... and still want to hang something with a huge surface area (germ growth, biofouling) into the network, completely without any requirement.