That diagram is not a factory diagram, it's from an aftermarket part catalog used by dealers. It can be trusted about as much as any news story you read on the internet. To find out how the emission system works you need to look in the factory service manual, and/or factory part catalog (MicroCat). I've never researched this so I don't know how the evap system functions, or if it has any connection to the engine vacuum pump.I stand corrected. That part number for the pump in that diagram pulls up the brake vacuum pump.
I also don’t why this would give white smoke at startup.
I guess OP could disconnect the purge valve from the air intake and see if anything is seeping. Maybe also start it and run it with the purge disconnected and see if the problem persists. Plug the opening on the intake side to prevent a vacuum leak and maybe plug the purge valve side to try to avoid an evap code.
You mentioned that the PCV was changed. I assume this was after the smoke started. How bad was the PCV - was it torn?
If your thinking of disconnecting the brake pump, be careful as that can be a bit dangerous. Your brakes will not work nearly as well without that pump connected. Might be okay to observe the startup smoke.
Not sure if you’re doing this work yourself or not, but you might just pull the intake manifold
I just don’t understand the mechanism by which that was happening.
Just spitballing here: If the pump "loses its seal" at higher RPMs and no longer creates vacuum. Then the oil could be leaking and pulled into the intake through the intakes vacuum since the pump is theoretically 'open'?