I'm not sure if there is a well-trusted authority on this akin to MBA but it is certainly a leading issue in the seafood industry. More governments are codifying an acknowledgement of animal sentience in various ways [1] and there is a lot of active research into the various slaughter methods used for ethical and quality reasons [2]. You can find a lot of research into existing and novel methods for "stunning" fish (i.e., rendering them unconscious to then slaughter), even the use of things like EEG to measure brain activity of animals [3]. This is not my area of expertise, but I think that the overall conclusion is that we could be doing a much better job of minimizing the suffering of animals in farmed and wild fisheries. The good news is that people are realizing that and working on correcting it.

[1]: https://www.theguardian.com/world/2022/oct/08/farmed-fish-fe...

[2]: https://www.globalseafood.org/advocate/fish-producers-benefi...

[3]: https://onlinelibrary.wiley.com/doi/full/10.1111/are.14857