Findings from psychology and related fields suggest that some aspects of human morality may have evolved and/or serves a social purpose among human groups (e.g., Awad et al., 2020). Thus, what is "good" depends to some extent on one's cultural background, to a greater extent on being human, and perhaps to an even greater extent on being a primate/mammal/vertebrate/etc (i.e., in terms of how features of our minds have been shaped over an even longer evolutionary time span). What happens if we try to think outside these evolutionary and social pressures? Many EAs try to think outside of social pressures, for instance, when they espouse utilitarism. If so, shouldn't we also try to "escape the shackles of evolution"? I'm hoping this question will lead to recommendations for readings that discuss what dimensions of "good" would be relevant from non-human points of view (including from other animal species, from ecosystems, from AIs, etc.)
You might check out this SEP article: https://plato.stanford.edu/entries/morality-biology/. Haven't read it myself, but looking at the table of contents it seems like it might be helpful for you (SEP is generally pretty high-quality). People have made a lot of different arguments that start from the observation that human morality has likely been shaped by evolutionary pressures, and it's pretty complicated to try to figure out what conclusions to draw from this observation. It's not at all obvious that it implies we should try to "escape the shackles of evolution" as you put it. It may imply that, but it also may not. (In particular, "selective evolutionary debunking arguments" seem to have implications along these lines, but "general evolutionary debunking arguments" seem to lead to almost the opposite conclusion.)
You might also check out this post by Eliezer.
Interesting! The philosophical debates about the nature of morality in light of evolution is a great literature, which I very much recommend checking out further. However, the main question of contention in those debates is whether studies of the kind you allude to in fact show anything about morality itself. In fact, the mainstream view in metaethics is that the conclusion, which you have included in the title question, that morality emerges from evolutionary and functional pressures, is false. What usually happens in those studies is that some evolutionary psychologist identifies morality with some trait they can easily measure, and draw a bunch of conclusions. The entry to SEP that Ikaxas mentions is an excellent introduction to these debates. I can also recommend the podcast 'very bad wizards', which features a philosopher and psychologist talking about issues such as these.