[Stretch Goal] Implement pagination on the game list page

[automagicallyio]

Description

Implement pagination functionality on the game list page to improve performance and user experience when browsing large numbers of games. This is a stretch goal that will enhance scalability as the platform grows.

Why This Matters

As the game catalog expands, loading all games on a single page will negatively impact performance and user experience. Pagination ensures the page loads quickly regardless of catalog size and provides a better browsing experience for users.

Acceptance Criteria

• Implement backend pagination in the games API endpoint
• Add pagination controls (Previous/Next, page numbers) to the UI
• Support configurable page size (e.g., 10, 25, 50 games per page)
• Display total number of games and current page range
• Maintain pagination state when applying filters
• Update URL with pagination parameters for shareable links
• Add loading states during page transitions
• Update tests to cover pagination functionality
• Ensure pagination works correctly with existing filtering