Allow users to filter games by category and publisher

[automagicallyio]

Description

Add filtering functionality to enable users to filter games by category and publisher on the game list page. This will improve user experience by allowing them to quickly find games that match their interests.

Why This Matters

As the game catalog grows, users need efficient ways to discover games. Filtering by category (e.g., Strategy, RPG, Puzzle) and publisher helps users narrow down their search and find relevant games faster, improving overall platform usability.

Acceptance Criteria

• Add filter UI controls for category and publisher on the game list page
• Implement filtering logic in the backend API endpoint
• Filter selections persist when navigating between pages
• Display clear indication when filters are active
• Show count of filtered results
• Include "Clear filters" functionality
• Update tests to cover filtering functionality