The ball(s) are Godot RigidBody2D nodes. Basically they are "dumb" physics objects. They are set up to collide with essentially every element on the board.
The flippers only apply a force on the ball when they are triggered. The balls still bounce/roll on the flippers when they are idle, but if the flipper is actively rising upwards and it is touching the ball, the ball will be pushed with a strong force applied perpendicular to the surface of the flipper.
Edit: The other important detail is that the force applied by the flippers increases the closer the ball is to the end of the flipper. Basically, hitting the ball when it's in the middle of the flipper is not very powerful, but hitting the ball when it's at the end of the flipper is quite strong.