The beam is not in good condition.
Although the spot is round, the unburned area in the lower left quadrant shows that the energy distribution isn’t correct over the entire beam. It should be more intense at the center and taper off symmetrically around the perimeter, which it does not.
The two pictures at Mirror 2 show the same shape, somewhat enlarged due to the beam spreading.
@jkwilborn’s post at his link shows the correct beam shape. Note the similarity of the beam shape from his “bad” tube to your pictures:
So the tube in your laser is not operating in TEM00 mode.