How to obtain mean Power Spectrum from two audio channels?
The sound pressure level (and derived metrics such as the SPL spectrum) are dependent on the position of the listener, since it is a measure of the pressure of the wavefront moving through space. As such it doesn't make all that much sense to try to combine SPL's from different positions into a single value, except perhaps if the listeners were exactly the same distance from a single omnidirectional audio source and there was no possibility of reflections.

The equations you have posted are for two audio sources, not two listeners, so I am not sure they are relevant.

The only value of any use I can imagine you being able to calculate from two listeners would be the peak SPL / spectrum, this would simply be the maximum value of both channels for any given sample.