Also, there are theories of FTL: https://en.wikipedia.org/wiki/Faster-than-light
Ah, no they didn't. Scientific consensus has been the earth is round for thousands of years.
I'm not arguing with your idea ... just that it should start with a caveat ... "there are no current theories that support FTL but we're hoping ..."
However, if the idea is that a laser that is continuously lit can "sweep" a path, such that the laser dot appears to move faster than light could travel that same path... Then of course that's trivially true. The light is traveling the radius of the arc, not the length.
Sure, this is correct, but I don't see how this describes anything traveling faster than light. The light spot itself is an effect of the light that's traveled to that point (at the speed of light). The spot "moving" is (physically) more of an illusion as the light now travels to an adjacent location.
As far as I understand it doesn't actually move
The light itself will continue to travel at normal speed but if you waited for the light to bounce back from distant planets you could observe the shadow moving FTL.