There was a legal case involving the wrongful death of someone in a boat that needed the boundary better defined for jurisdictional reasons and some older documents said “the whole watercourse” was part of NSW: https://www.austlii.edu.au/cgi-bin/viewdoc/au/cases/cth/HCA/1980/11.html

It follows the middle of the river for part of it and the southern bank for the rest.

This isn’t zoomed in enough to show that the squiggly border is the middle of the river between SA and Vic. but the south bank of the river between NSW and Vic.