"Push a bucket into a pool of water", then stop and hold that static situation. Even though we have stopped the downward motion of the bucket, there will still be an upward force on our hand. That is buoyancy. It is caused by the difference in density of water and the air in the bucket and the effects of gravity causing the denser fluid to exert more pressure than the air inside the bucket. No velocity involved. Buoyancy is a force and there are calculations for it in Newton's.The spoon trick is to demonstrate how the wrapping of the water around the spoon, contrary to what you may expect, attracts the spoon the in direction of the curve. i.e. the water wrapping around the rail in the long spiral along the rail.
The displaced water is where you can see the rail engaged into the wave face. I wouldn't say "pushed down", more like it just got moved. Push a bucket into a pool of water. The resistance you feel is the weight of the water that was pushed out of the way.
Hence the term "throwing buckets"
"throwing buckets" - that's different. That's accelerating a mass. It creates inertial forces due to a change in velocity of that body of weight. Apparently just changing the direction of mass is also a form of acceleration e.g deflecting water down at the spray root from angle of attack in the entry rocker or water wrapping the rail like you said.
So there will be a combination of a buoyant force and inertial forces on a moving surfboard. We disagree on the magnitude of the buoyant force, I say not much and that most of the lift comes from the inertial forces.