I've been banging on about this for years, but it's not something most people want to hear. Free range chicken and egg production can be devastating. In some respects even worse than intensive indoor production, which is another kind of nightmare. https://www.theguardian.com/environment/2020/jun/20/its-like-pea-soup-poultry-farms-turn-wye-into-wildlife-death-trap

Free range is less abominably cruel to the chickens than entirely indoor production. But because its impacts are not contained, and because the feed requirements are higher, its environmental credentials tend to be even worse.

In both cases chickens are fed on maize, wheat, soya, palm oil kernel, fish meal etc. To understand the environmental cost of eggs and chicken meat, you must multiply the impacts of the feed production by the impacts of raising the chickens.
Free range does not = conscience-free

In all cases, the conclusion is inescapable: if you want to reduce the impacts of your diet, the answer is not to eat different kinds of meat or eggs, but to eat much less of either.