I do nut hunt in a stand, and have not used ropes in that way.
I spent years rock and ice climbing, and used ropes in that way, For my personal satisfaction, and as a licensed guide.
I'd use ay least an 8mm anchor line (plenty adequate for strength), and a significantly smaller diameter prussic line ( if I used a prussic), or more likely what I have on hand, and am accustomed to using… a 10mm -11mm anchor line, and standard prussic diameter of 6 or 7mm. The smaller diameter of the prussic cord is part of it's ability to cinch on the anchor line.
Hope I said that in a way that makes sense.