Mines also go up through the wall to the 2nd floor and exit the water the the washing machine drain.
I use this system here
Had it for 1.5 years now and no problems.
I test my water hardness using test kit and I am getting about a reading of 5 PPM. Without the softerner, it was 250 PPM
I bought a Lennar home so the plumbing was already pre-plumb in the garage for a water softerner. Lennar also pre-plumb the kitchen sink for a reverse osmosis system.
I bought this system off Amazon Here that comes with both the water softern and reverse osmosis system for $749 at the time.
Got it installed by a handy man for both system for $300 labor
Total cost $1049
Had it since April 2021 and both system is still going strong. Super happy with it and SUPER HAPPY I didn't get suck into buying system from kinetico ($7000) or a plumber for (3-5K)
I test my water softness using test strips and I get about 5 PPM for hardness now. Regular tap water is about 250 PPM