Why are photons reaching us from the Andromeda Galaxy not the same photons that left the Andromeda Galaxy? Is that because photons from the Andromeda Galaxy interact with intervening dust clouds or other matter on their way to Earth? Or do you refer to particle physics (light on light scattering, photon-photon collisions to produce electron-positron pairs, or the reverse reaction) or quantum effects (virtual photons)? In any of the latter examples, "new" photons from M31 arriving at my eyeball would not contribute to the sharp optical image of M31 that my brain or my camera sensor creates.
M31 is very nearby on the cosmological scale and is approaching us, not receding. All photons escaping M31 in our direction (allowing for 2.5 million years of galactic motion) should reach us unless something happens to them en route.
If Earth is at the center of a sphere, at what radius do objects recede from us due to cosmological inflation at faster than c, so that their photons can no longer reach us, nor ours reach them? Would that be 13.8 billion light years? This idea is difficult for me to conceptualize because the hypothetical sphere in the question is defined within space-time that is not fixed, but expanding. There aren't many opportunities to get intelligent answers to these questions, so thank you.