Assuming the test pattern ran at about the same speed as the problems shown in the first picture, it rules out gross mechanical problems. The Y axis has a slight wobble, but that may be mechanical flexing of the heavy laser head on the (small) X axis bearing follower and is likely not fix-able.
The key difference between the test pattern and your design is the laser power: minimal to mark cardboard, 90% to cut plywood.
Based on that, I think this is another instance of USB communication glitches, because errors / dropouts will trash parts of the commands controlling the laser head position.
Higher laser power can cause both power supply brownouts and USB glitches. Unfortunately, there are no definitive tests to isolate the problem or verify the solution, so it comes down to trying a few things to see if the situation improves.
Some previous discussions provide suggestions:
Protip: Use cardboard until you’re certain the problem is resolved.
