Following on from my question here: Clarification on quotation sources around Sanhedrin 57a
All citations (that I can find through Jewish resources linked in the original question) that claim to refute or debunk the mentioned Sanhedrin 57a tract and the related Gemara - https://www.sefaria.org/Sanhedrin.57a.16?lang=bi&with=Mishneh%20Torah,%20Murderer%20and%20the%20Preservation%20of%20Life&lang2=en "...wherever there is liability for capital punishment, this tanna teaches it; as it is taught in the first clause: With regard to bloodshed, if a gentile murders another gentile, or a gentile murders a Jew, he is liable. If a Jew murders a gentile, he is exempt."
- seem to indicate leaving the judgement of a Jew who kills a (Noahide) Gentile 'up to the hand of Heaven'.
I've seen it claimed that this means a Beth Din had no jurisdiction over cases involving Gentiles; but in contrast a Gentile can be tried in a Jewish court (and are more liable to receive the death penalty than a Jew involved in the same crime - see citations on Maimonides 42-45 here: https://matzpen.org/english/1981-10-10/the-jewish-religion-and-its-attitude-to-non-jews-appendix-israel-shahak/#fn-208-45) AND we apparently shouldn't hand over a Jew to a Gentile court (if he will lose). I also can't find that some other non-death punishment such as lashes or a fine applies either.
I'm very worried about not being able to properly refute accusations about this from antisemites who cite these passages; especially when some fundamentalist Rabbis use them to promote violence and unequal justice as well.
Is there ANY halachic text specifying that a Jew who murders a (Noahide/righteous, with whom we are not at war/oppressed by, since with idolaters or enemies this is even less likely) Gentile (including when we will in Israel with a Beth Din, etc) IS to be punished in a human court and not just left up to Heaven's hand (ideally even when there is neither 'concern about inciting hatred', nor 'risk of desecration of G-d's name' involved)?