I'm not sure exactly what the specific story is about hair pins and watches. It could be a story where a hair pin is used to fix a broken watch strap, or perhaps a more magical story where a hair pin has some special power related to a watch, like opening a secret compartment in it.
A hair pin could get stuck in a watch mechanism. For example, if a person is wearing a watch on their wrist while doing their hair and the hair pin accidentally slips into the watch. This could cause the watch to stop working.
Perhaps in the fanfiction, the black hair tie on Jade's wrist is a clue to her past. She has amnesia and the hair tie is the only thing she has from her previous life. As she begins to investigate, she meets various characters who either try to help or hinder her in uncovering the secrets associated with the hair tie.
One reason is the complex relationship between Snape and Harry in the original Harry Potter series. Writers are intrigued by this relationship and use the idea of Snape pinning something on Harry as a way to explore it further. It could be a symbol of protection, a sign of a hidden connection, or a device for plot development.
Queen Pins is not based on any actual events or people. It's the imagination of the writers and creators, crafted to provide an engaging and fictional narrative for viewers.