Thanks for the translation !
Here is how I interpret the "kodoku" frog as it's written here.
TLDR; it's a frog that managed to survive competition against other frogs
Kodoku (蠱毒) refers to an ancient practice in China where a sorcerer would place a hundred poisonous snakes/centipedes/frogs in a sealed jar. The last remaining animal would have the strongest poison, since it ate/killed the others.
It would then be used as an ingredient for various purposes : cursing someone, manipulating them...
Kodoku here refers to the part where the last remaining frog is the strongest.
I would translate kodoku frog as "lethal frog" perhaps. That way, we can keep the dialogue about Tsugumi wondering if it's poisonous, and have Hitaki explain that it's a frog that survived the competition in the wilderness.
For example, chapter 48 of the action manga Sousei No Onmyoji/Twin Star Exorcists references this directly. Here, kodoku is a ritual to create the strongest exorcist. Be warned, it's quite explicit.