Moving wall / cube pushes player in steps and not smoothly, how to fix? [SOLVED]

Yes, that is exactly what is happening in the first vid. Having a separate camera actor moving at its own pace should be helpful down the road, like encountering a mini boss at the end of a level and the camera stops and the player is forced to stay in one screen sized box with mini boss.

The OP’s original question and goal was to make a Gradius style game, in that case the ship or craft is pulled along if the player goes all the way to the left of the screen (for old CRT TV there was probably a safe zone there). I doubt that Konami was using the exact same mechanism as a wall for that effect (perhaps a boundary of some kind though), but in UE4 I imagine it would have to be done. But like you, at this point I’m starting to think there might be another way to achieve this.

This pic below, I think would work. As the player’s capsule overlaps the wall, the capsule receives an offset positive in the Y matching the wall’s speed. This code is in the third person character BP, so I just need to get a reference to the moving wall to plug into is overlapping boolean.