To confuse things even more, I believe the book says that while the initial powerup of the flightdeck is a FO task, it can be performed by the captain if he/she is the first to the plane. So basically, whoever walks on the plane first does that very first flow.

During training, the trainee in the captain seat will do the cockpit prep flow while the trainee in the right seat, who's PF for the "flight", does the FMS setup. We discovered it's a huge time saver and allows us to get off the gate in like 10 minutes.