1. You state clear water comes out when black flushing.
2. I assume you also mean that when you installed the blue tab NO BLUE WATER came out
3. What you have is simple. It is NOT a poop pyramid. If so, the toilet water flush would mix and you would get dirty water not clear
4. The flush nozzle is either down from the top of the tank on the Passenger side or at the 3/4 to full mark on the SIDE of the tank on the passenger side. That means IF it is obviously working(clear water out the exit fitting) then if a Poop Pyramid, would hit some of the pyramid and would be dirty water not clear.
5. The simple solution is you must have a 3 inch ABS tube from the bottom of the toilet floor flange to the top of the tank. This tube is probably NOT straight but has 1 or 2 angles to it and this has caused debris to clog up that down tube. NOT all the way, but probably 90% or more. This is one of the times(about the ONLY TIME) you can use a standard handheld toilet snake and insert down that 4 to 18 inches to break the debris loose. BEFORE you start, pour about a gallon of boiling water thru the toilet to help soften up the debris. Doug
PS, IF you do have a Poop Pyramid, this tool will also help break up the pyramid
https://www.lowes.com/pd/Cobra-3-8-in-x-3-ft-Music-Wire-Toilet-Auger/1001845024?cm_mmc=shp-_-c-_-prd-_-plb-_-ggl-_-LIA_PLB_208_Plumbing-Repair-_-1001845024-_-local-_-0-_-0&ds_rl=1286981&gclid=CjwKCAjwve2TBhByEiwAaktM1LnBFBY8apJ5ZQ363Duf5I536wZ1pF0bAv5l042r2YJ4nfhVKEfoGRoCxzcQAvD_BwE&gclsrc=aw.ds