Hey Zack,
I'm glad you're going to tackle a search feature, I love keyboard bashing and a search bar makes a good victim.
So you might need to brush up on Backbone (its relatively simple structure of javascript apps) It uses MVC ( I hope you're familiar with the acronym - model-view-controller) pattern.
Take a look around at implementing a filtered search bar in backbone.js, someone must have done something with like that it the great internet.
Once you have a rough idea on how it might be implemented (or even during, if you're like me and impatient) you can look at the structure of swagger-ui.
It's not a friendly place, so take care not to get lost. It's in need of an overhaul, but as it's relied on by quite of few people, thing have to be done slowly.
It might be a bigger challenge than one would initially think. Perhaps you can start by adding to an existing feature.
There is an apiSorter function, which sorts the apis. You could start with the search bar, that on change it would change the function and re-render the views.
We'll be here to help where we can (ron always has wisdom, if not Javascript prowess)