With your example, nothing is “moving”.

Imagine a giant wave in the ocean that is almost lined up perfectly parallel to the shore. Imagine the angle that the wave is off by is astronomically small (0.0000000001 degrees off from parallel). Also imagine the shore line is astronomically long (millions of kilometers).

One end of the wave will crash the shore slightly before the other end of the wave at the opposite end of the shore. The difference in time between the two sides of the shore is also astronomically small (so small that not even light could reach the other end in time)

Now let me ask you: did the wave “crash” travel faster than the speed of light? Of course not. I think that is a similar analogy to the laser movement concept you described.

Edit: Fun thought experiment. Depending on where you are on the shore (which end you are closer to), you may see one end crash before the other end (one event happening before the other event). Have two people at different locations on the shore, once they meet up with each other, they might disagree on which end crashed first! And they would BOTH be correct! Relativity is fucking crazy