As for me personally whether SRT basal/ or Ddrt I want a trees branch that is at least as big around as my calf. That has been a safe rule of thumb for me personally.
If you are connecting a canopy anchor that will girth hitch the entire tree, the size of the branch truly isn’t important, as it’s only supporting the weight of the rope temporarily while you pull the pull line and rope into position. Once the rope is girth hitched and pulled snuggly, the entire tree is supporting your weight, not just the crotch of the branch. I hope that makes sense
I will edit this to also mention, be sure to check the back and sides of the tree for little splinter branches or twigs that may keep your girth hitch from fully cinching. I bounce on my rope several times at ground level to be sure my rope fully cinched, Because when they break while you’re climbing, your butt ends up puckering pretty badly from the fear of that surprise 8 or 10” sudden drop while the rope finishes tightening….