Add a search box to find games by title

Players who already know what they're looking for shouldn't have to scan the whole catalog. Adding a simple search box on the game list page lets users quickly narrow the list by title, improving discoverability alongside the planned category and publisher filters. This builds on the existing game list data layer without changing the data model.

Acceptance criteria

• The game list page includes a search input that filters games by title
• Matching is case-insensitive and updates the visible list as the user types or submits
• An appropriate empty state is shown when no games match the search
• The search input follows the project's accessibility guidelines (labeling, keyboard navigation, visible focus states) and includes a data-testid attribute
• Unit tests cover any new data-layer/search helper and Playwright e2e tests cover the search behavior

Start at the game list page and its existing game list data layer, then trace how the visible game collection is rendered. Add the title search behavior, accessible input, empty state, and data-testid described in the acceptance criteria. Run the relevant unit tests and add or run Playwright coverage for typing or submitting a search and displaying matching and empty results.