Wow! Surprising speed. I tried to make cigarettes myself, but I couldn't make the perfect cigarette anyway. I had to give up and chose a cigarette maker. This is a better choice for me, ha ha ha ha.
Water filters do not seem to be able to soften the water, only efficiency water softener system can. The effect of hard water is that kettles fur up, taps normally get deposits on them and boilers to become less efficient. We have one that does the whole house, there are no downsides other than...
I think you should change to a better quality water softener. Like Fleck or Aquasana, especially Aquasana. If you are using well water or tap water, it is the most suitable.
I have to admit that water quality has a huge impact on beer. In other posts about brewing, I saw that many people have lost their beer quality because of moving and using water softeners. I don't know if they have solved these problems in the end. My point is that you'd better do a water test...