The product team identified that users were not utilizing filters in the search interface due to a lack of awareness of their existence. To address this, they rebuilt the user interface to highlight filter functionality, which involved managing focus, ensuring only one filter menu is open at a time, and triggering a new search when a filter is selected. They tackled these challenges using React's Context API and refs, creating a centralized system to manage menu states and input focus. The Context API avoids prop drilling by passing data and setter functions down the component tree, allowing child components to update the parent component's state and re-render with new visibility. Refs, although considered an antipattern, were used to directly access DOM elements for input focus management. This approach allowed for better focus state management and a more consistent user experience, decoupling business logic from UI presentation, and simplifying code readability for future developers.