I'm not confused?
Seems clear the OP is just saying he knows how a JB4 should work (steering wheel controls) and he has tried that to see if his car has a JB4 fitted. The SW controls don't go into JB4 programming mode so he is assuming from that there is no JB4 fitted.
He says he has had the CEL lights before (sometime previously) and they went on startup, so could be any fleeting occassional errors - it is a 56 car.
But OP - it could be a flash program (chip) not a JB3/4, I still think amongst the masses, the JB4 is a minority option, there are so many garage 'chip tuners' offering cheap off-the-shelf flash upgrades now, amongst the general car enthusiast public piggbybacks (JB4) are a bit of a dirty word.
You need to go back to the dealer you bought it from, if they have sold you a chipped/JB3/JB4/Flashed/modified car (it probably happens all the time) they need to sort it out.
E90 330i 6MT gone. E91 335i 6MT gone. AMG E63 Estate gone. M6GC current...