I understand the upper stage separates with the use of pneumatic pushers, but what settles the propellants in the upper stage tanks so that the propellant is pushed back to the intake? The pushers will cause the propellant to initially be pushed to the back of the tank, but won't it immediately begin to slosh towards the front of the tank? Is there a baffle design or something inside the tanks that keep the propellant at the intake?
It uses the cold nitrogen gas RCS thrusters. Sometimes, you can see them firing shortly before second stage engine startup.
Elon Musk has talked about using the ullage gas vents as RCS thrusters and for propellant settling as well. He mentioned they are already using them to help deorbit the second stage. Super Heavy will not have separate RCS thrusters, it will use ullage gas instead. SpaceX might do the same with Starship.