Could be plugs or coils by now also. Why throw the least likely cause at it, injectors?
I would probably throw the EGR sensor at it first as stated above. Also the systems are not that good at catching light or lean misfires. I had a very slight miss at about 25k, no light. Replaced spark plugs...
I believe your new battery will run out of warranty when the regular warranty runs out. Parts replaced under warranty don’t start the warranty clock over as far as I know.
We will never know all the facts to this case. Making engines run “efficiently” is not the same as making engines run without cancer causing pollutants. Guilty as hell and got away with it.
Mine looked like that except a little worse and there was some minor cracking . I just replaced the rotors and reused the pads, they looked fine probably 75% left at around 25k miles.