Your intuition isn’t far off; there is an angle where the weight of green relative to the sum over wavelengths sees a local maximum. But it doesn’t dominate. In that transition zone, there is still an overlapping, transitioning abundance of redder and bluer wavelengths, adding with the green. Consequently, you see red, going into a red+green transition (== oranges, yellows), go into into a green+blue transition (== cyan), which already has few photons relative to the red and yellow zones, so it’s a dark/weak cyan, before it blends into the darker blue of the night sky.

Because the color of the sky is determined by a shifting mixture of wavelengths, not a single shifting wavelength.

Basically, the scattering process that "remove" blue from the spectrum also removes green, albeit to a lesser extent. There are some greenish and yellowish wavelengths in the sunset sky, but they're dominated by red, so the overall color appears red or orange.

In order for the sky to look noticeably green, there would have to be something that scattered reds and blues, without significantly absorbing green.

If you try to interpolate between sky-blue and orange using graphics software, the result depends on what "color space" you're using. If your software interpolates based on hue, you might see green (or purple) in the middle. But that's not physically realistic.

A realistic model is to interpolate each wavelength of the continuous spectrum separately. Interpolating in RGB color space is a crude approximation to this. And if you try the experiment, you'll see that the midpoint between sky-blue and orange is a kind of muddy brown, not green.

You won't get a green sky, but at least there is a meteorological optical phenomenon called the green flash around sunset. To see it, I think, you have to know what you're looking for - and you need good conditions.

It can be - https://en.wikipedia.org/wiki/Green_flash

Blue + Green + Red = White

Green + Red = Yellow

Red = Red

That is the natural transition from overhead sun to sunset as each higher energy wavelength gets cut off more and more. When blue is mostly gone and green starts to fade we call it the Golden Hour.

The explanation that made it click for me a while ago was by someone who implemented a shader https://www.alanzucconi.com/2017/10/10/atmospheric-scatterin... — the explanations that don't end up producing an image all seemed to skip over one detail or another.

I think at this point you need to consider how the human eye see color. It's not like each wavelength gets picked up and then communicated perfectly.

(I'm going to skip over some basic stuff, and use some generalities)

Each Cone in the eye responds to a range of frequencies. This means that things that unless it's on the extreme low, or high, end of the frequencies that the human eye can discern you are going to have two, or all three, Cone types responding. The strength of those responses is what your brain uses to interpret the color that you see.

The real problem is that out in space there is no attenuation of sunlight, it's bright. Super crazy bright. It basically overloads all of your Cones, and Rods, all at once, there is no way for your brain to find a signal of "oh there's more higher wavelengths here so interpret bluer than normal" because all of the signals got maxed out. If you max out all of the signals, you get white. It doesn't matter that in absolute terms there's more blue, the lower and mid frequencies are also maxed out.

Perhaps because one's world is often blue-lit? While whole-hemisphere illumination generalizes as warmer, local conditions vary. Absent direct (yellow-ish) sunlight, outdoor daylight illumination can be quite blue-ish. I've had fun recently with photos in a park under clear blue skies, shadowed by tall buildings... but with a gap, resulting in a narrow strip of bright sunlit ground. My phone will take a bit of sunlit snow as its whitepoint, and provide a blue-tinted world. Similarly for sunlit buildings in background.

Is it considered a warmer color on the surface?

Mid-day sun in a clear sky is very white, in the 5k-6k color temperature range. It's hard to get a sense of how white it is because of how bright it is. In fact, the color temperature on the surface can be even higher than in outer-space!

Compare this to a "warm" light bulb, which is around 2.5K. Sunrise/sunset is also around that range.

Perhaps the "warm color" sun mindset comes from the only times that people can look directly at it. That is to say, around sunrise or sunset.