Build the exercise library page with a search-first layout: a prominent search bar at the top (searches exercise name), with filter chips below it for exercise_type (strength/cardio/mobility) and primary_muscle (chest, back, legs, etc.) that users can tap to narrow results without needing to know the exact exercise name. Filters should be multi-select and combinable with the search text. Show results as a list/grid with name, type, and equipment. Custom exercises (is_custom=true) get a small "Custom" badge. Make it mobile-friendly with large tap targets for the filter chips. Type filters and muscle filters can be AND'd together.

*Claude says to make styling decisions before this step