I think you are wrong about it being a carbon filter. You don't regenerate carbon and to use the bleach, the filter has to regenerate. Carbon is only backwashed.
I think you have a Pyrolox filter, they (can) use bleach. Or it's a manganese greensand filter. Greensand is the only mineral that commonally uses potassium permanganate, a serious poison.
Never mix potassium permanganate with anything but especially not with chlorine or Iron Out or similar products.
Bleach sitting in a non sealed tank will weaken substantially, especially over 3 months. Replace the bleach and start a manual regeneration. When the control starts to suck bleach, watch it and just before the bleach runs out, unplug the unit for 20 minutes. Then plug it in and when it goes into backwash, unplug it and let it backwash for 15 minutes and plug it in again and let it finish from there on its own. That may or may not clean the mineral.
BTW, carbon also absorbs 'contaminants'.