The nastiest piercing Wynn examines seems straight-up designed to mindbreak its wearer; any thoughts more complicated than immediately obeying orders will be punished, and the harder they're trying to think the worse they're punished, presumably with the end goal that the wearer just stops having thoughts. They're surprisingly intricate work for what amounts to a couple inches of brass plate with a piercing hook mounted, but every bit of the space available is covered in tight, efficient runework, and between the set of them, there's a lot of patterns for using runes to sense various mental states. They'd probably make a little more sense to Wynn if she was familiar with mental magic, but if she wants to make magic items that trigger from mental actions, there are pieces of the solution she wants here, if she's got the stomach to disentangle it.
Exposed to Wynn's examination, the collars have a lot of similar workings; they're designed to sense something like the mental states of obedience and disobedience. The former is rewarded with... happiness, fulfillment, satisfaction? The latter is punished with... physical and emotional pain? There's a lot to examine, but the fancier collar seems like an elegant and complex tool for gradually conditioning the wearer to only truly feel satisfied when they are obeying orders to the best of their ability, and to make any disobedient action or thought unpleasant enough to be not worth considering. The fancy collar also seems much older, and much more permanent, than anything else from the heist... more like Wynn and Luna's "Isekai items" and less like the kind of stuff she's figured out how to slap together. The cruder collar seems like a fragile amateurish attempt at recreating the fancy artistry of the first with more legible techniques, trading a lot of the subtle elegance of the former's reinforcement patterns in favour of hitting harder with its highs and lows, and draining the wearer's mana pool to sustain itself. A lot of the rune sections on both collars are weirdly illegible, but with the fancy collar it feels more like tracing a bunch of really complex interactions written in machine language, and with the latter it feels more like trying to follow some hack of a programmer's deliberately obfuscated code.
That said, there's definitely a lot of similarities between the confusing loops of the cheap collar's runework, and the complex patterns of the branding poker. It's like the rod is a piece of a puzzle the collar represents, and its purpose is to provide a very specific signal that the collar is looking for so that the collar can do... something? Carefully examining the rune-chunk on the actual branding part, it seems to line up well with similar rune-chunks at the ends of the collar. So if the collar were to be closed around someone's neck, the poker would best fit into the runework if placed right across the gap.