What is the origin of the transferred oxygendianion in redox reactions?
I think you are misunderstanding the meaning of superoxide and the rules.

Superoxide is $\ce{O_2^-}$

Superoxide is NOT $\ce{O^{2-}}$ as you have written.

The rules are referring to hydroxide which is $\ce{OH^-}$, not superoxide.

The reason hydroxide is used to balance equations in basic aqueous solution is:

$\ce{H_2O \leftrightharpoons H^+ + OH^-}$

There is hydroxide present in aqueous solution, but not superoxide, peroxide, hydroxyl radial, etc.