Add product search functionality

Description

Implement a comprehensive product search feature that allows users to find products quickly and efficiently by name and category.

Acceptance Criteria

Search by Name

• Users can enter text in a search input field to search for products by name
• Search should be case-insensitive
• Search should support partial matches (e.g., searching 'Smart' finds 'SmartFeeder One')
• Search results should update in real-time as the user types (with appropriate debouncing)
• Display a 'No results found' message when search yields no matches

Search by Category

• Users can filter products by category/type (e.g., Feeders, Entertainment, Health Monitoring, Accessories)
• Category filter should be easily accessible (dropdown, chips, or sidebar)
• Multiple categories can be selected simultaneously (optional enhancement)
• Category filter should work in combination with text search

User Experience

• Search input should have a clear/reset button to quickly clear the search
• Search icon should be visible next to the input field
• Loading state should be shown while search results are being fetched (if async)
• Previous search query should persist when navigating back to the products page
• Display count of search results (e.g., 'Found 5 products')

Performance

• Search should be performant with large product catalogs
• Implement debouncing (250-300ms) to avoid excessive API calls
• Consider client-side filtering for initial implementation if dataset is small

Technical Implementation

• Add search parameter to URL query string for shareable search links
• API endpoint should support search and filter parameters
• Implement proper error handling for failed search requests
• Add appropriate ARIA labels for accessibility

No files, tests, or entry points are named. Start by locating the products page and the product API or data source, then trace existing filtering and navigation behavior. Done means the stated name, category, URL, loading, error, accessibility, and performance criteria are implemented and verified.