There is a debate about "how reducing" the atmosphere of the early Earth was, and this question is my attempt to grasp toward an understanding of what that that phrase really means. As a bit of context, the Miller–Urey experiment produces a wide variety of complex organic molecules, but people say it requires a very reducing atmosphere to work, and it's disputed whether the early Earth's atmosphere was reducing enough for analogous processes to occur. Ultimately I would like to understand what it is about reducing atmospheres that allows complex organic molecules to be created so easily, but the first step is to understand what it really means to say one mixture of gases is "more reducing" than another.
If anything can be more reducing than something else, it seems like $\ce{CH4}$ gas should be more reducing than $\ce{O2}$, so I'm trying to understand the extent to which this can be quantified. However, I'm currently self-learning chemistry, and I'm having difficulty seeing connections between some of the concepts. (So apologies in advance for the rambling nature of this question.)
It seemed like one place to start might be to draw the net reaction of methane oxidation:
Obviously, if you add up the total oxidation state of every atom, you get zero - the carbon gets oxidised, the oxygen gets reduced, and the hydrogen stays the same. This must always be the case for any reaction (right?) since electrons are conserved. At first this made me think that maybe you can't really say that one thing is objectively "more reducing" than another. Though of course you can still talk about its tendency to oxidise or reduce carbon, and maybe that's what people are talking about when they say an atmosphere is "reducing" or "oxidising".
But then I came across the concept of redox potential, which does seem to be about things being objectively more reducing or oxidising than others. The problem is, the discussions of the concept that I can find online seem to be in terms of electrons "being transferred" from one molecule to another. But in the reaction above, as far as I can see, electrons aren't being transferred from the $\ce{O2}$ to the $\ce{CH4}$ but instead both molecules are being destroyed and replaced with completely different ones. So I'm having trouble seeing whether, or how, the concept of redox potential can be applied in this case.
Given this confusion, I guess my specific questions are:
When people talk about an atmosphere being "more reducing" than another, are they referring to redox potential or something else, such as the degree to which the atmosphere reduces or oxidises carbon? If it's the latter, is it something that can be quantified, or is it more of a subjective judgement?; and
What is the relationship between the concepts of the redox potential of a substance on the one hand, and the oxidation states of atoms on the other? Can the concept of redox potential be applied to gases like $\ce{CH4}$ and $\ce{O2}$?