What exactly does it mean if someone has 142 arc degrees of stereo on the circle test? What is that person was planning to pursue ophthalmology?

That is okay stereo.

The fly test where patients try to grab the wings is at least 3000 seconds of stereo.

Titmus stereo acuities for the circle test are:

800 sec for 20/200 stereo VA
400 sec for 20/100
200 sec for 20/80
100 sec for 20/60
80 sec for 20/50
60 sec for 20/40
50 sec for 20/30
40 sec for 20/25

I am not aware of any studies stating how many seconds of stereo one needs to be an ophthalmic surgeon. I can only guess that you would want someone with at least 40 sec of stereo acuity to peel membranes of a retina, but another surgeon with 142 sec can do cataract and anterior segment surgery. Only my guess.