First, what "cosmologist think" and what we actually know are not completely identical.
Second, light has been described as having a dual identity as a wave and a particle, because sometimes it displays behavior like one but not the other, and other times is does the exact opposite. We call that behavior "paradoxical" and have adapted our thinking to whichever effect we actually detect.
So, when we are trying to answer a question like the OP, where "light" is considered to be a single photon with a specific energy, and then ask what happens when the space occupied by that photon is stretched, we should not be at all surprised if we get different answers when we treat the photon as a wave and a particle.
What we really don't understand is (1) what light is, and (2) how space "stretching" (if it really does that) would affect whatever light is.
Theorists try to think of photons only as waves in a "field" that permeates all of space. Engineers tend to think of fields as the maps of the effects created by the particles. It is a question of which is the primary entity and which is the effect of that entity.
So, when space "stretches", what happens to the fields and particles? Do they stretch, too, and if so, how? You can't just assume that we know that answer and then use that assumption to prove that energy is conserved or not conserved when space stretches.
What we really need is an experiment that demonstrates that space is actually stretching and also allows us to observe the effects of stretching on things like the behavior of photons, electrons, baryons, etc.
Regarding the thought experiment where we "gate" a single photon that originated in light emitted by a star billions of years ago, the real question comes down to how do we affect the outcome by the experimental setup. Given that we can "gate" individual photons in a diffraction experiment and get 2 different outcomes (different patterns of light effects on a target surface), depending on the experimental setup, we really can't predict what the effects of the hypothesized experiment should show without arbitrarily picking our expectations of whether all of the light emitted by the distant star is just independent particles (photons) or interdependent "waves".
Yes there are "true believers" of various theories. but I am an "agnostic" thinker who basically believes that "true believers" are simply being blind to what they don't understand.