Everyone (myself included!) who builds a CNC machine develops a huge blind spot when it comes to finding problems in its hardware. We’ve already looked and found nothing, so it must be a software problem.
Judging from the test, the X axis has many millimeters of backlash and the Y axis has a few. This is most likely due to a loose setscrew in a pulley or shaft coupler.
A copy-n-paste from a recent thread:
Start at the X axis motor, find each setscrew, and try to loosen it with a gentle counterclockwise turn: if it wasn’t tight to begin with, it will be very easy to loosen.
When you find the loose screw, loosen it by one turn, then rotate the pulley or coupling around the shaft while tightening the screw. Finish tightening it so it’s centered in the flat part of the shaft and firmly snug.
Then do the same for the Y axis.
There can be other causes, but look for the simplest ones first.