I’m not sure that either a failing battery or bad starter would cause white smoke. They would contribute to the car not starting depending on how it’s not starting.
Does it turn over but not fire? Does it not turn over at all?
You could try making sure the battery is fully charged and see exactly how that effects what happens when you try starting the car.
The old paper clip trick. Good on ye’. When the starter went out on my evoque there was a lot of white smoke as well. Threw me for a loop.
Excellent diagnosis BeastMode. Get that truck cranking and check compression (@ TDC this is critical). Get those readings to me and I’ll get them scrutinized.