There is no gold key but you will get 2 keys for doing it on vet hardmode. That's what people refer to as "gold pledge/gold key" because you used to get gold key for those and silver for non vet but they've changed that.

To activate hm you need to read the book near Kena (it will only be intractable on vet mode). This will make the lightning walls she summons move quite a bit faster.

There're similar hardmodes in all vet dungeons. Some are less obvious, original vet dungeons (those with II in their name) generally have HMs not related to books, such as having to keep 4 students up until Nerien'eth picks the sword up in COH 2 for example. All I/no number dungeon HMs are just "slap more health and damage on bosses and call it good" kind of things, with DLC ones having bit different mechanics in HM(faster lightning on Kena, moar meteors+portal feedback on Warden, less open doors on Veli, Stoneshapers ads on RoM last boss whose name I can never remember).