Finding the axis of an O

Yes, no more complicated than this!

An imaginary line drawn from top to bottom of a glyph bisecting the
upper and lower strokes is the axis.
Source: https://typedecon.com/blogs/type-glossary/axis/

It’s one thing to draw the axis of an existing font vs. designing a font with a coherent distribution of thicks and thins throughout.

If you’ve ever tried using a flat calligraphy nib, you’ll have noticed that thicks and thins are distributed differently depending on the angle at which you are holding the pen.

Typically, the axis on the O will help identify different type families in the Vox-AtypI classification…
As explained in http://www.typographher.com/glossary :

A completely vertical axis results in a neutral, upright posture. When
the axis leans left or right the letterforms have (positive or
negative) stress. Often in old-style typefaces the axis is more
inclined, and in transitional and didone faces, it’s vertical.
Rational and geometric typefaces often have a neutral axis (and
stress).