I just found a recent legal article about it: https://lawpublications.barry.edu/cgi/viewcontent.cgi?article=1187&context=barrylrev

Still didn't read it but I'll post a TLDR when I finish skimming through it.

TLDR: it's not codified and the claim that the US inherited the full body of English Common Law at the time of the secession (including trial by combat) is generally not accepted. There's no explicit decision of the supreme court but it's very unlikely it's actually legal in the US.