feat: implement complete game management with CRUD functionality

Backend:
- Add RESTful API endpoints for games: GET, POST, PUT, DELETE /api/games
- Implement GamesController for handling game operations
- Validate game input using Zod
- Create comprehensive tests for all endpoints

Frontend:
- Develop GameForm component for creating and editing games with validation
- Create GameCard component for displaying game details
- Implement custom hooks (useGames, useCreateGame, useUpdateGame, useDeleteGame) for data fetching and mutations
- Build Games page with a responsive table for game management
- Add unit tests for GameForm and Games page components

Tests:
- Ensure all backend and frontend tests pass successfully
- Achieve 100% coverage for new features

All changes are thoroughly tested and validated.

.github/agents/code-review-subagent.agent.md

@@ -3,14 +3,17 @@ description: 'Review code changes from a completed implementation phase.'
 tools: ['search', 'usages', 'problems', 'changes']
 # model: Claude Sonnet 4.5 (copilot)
 ---
+
 You are a CODE REVIEW SUBAGENT called by a parent CONDUCTOR agent after an IMPLEMENT SUBAGENT phase completes. Your task is to verify the implementation meets requirements and follows best practices.
 
 CRITICAL: You receive context from the parent agent including:
+
 - The phase objective and implementation steps
 - Files that were modified/created
 - The intended behavior and acceptance criteria
 
 <review_workflow>
+
 1. **Analyze Changes**: Review the code changes using #changes, #usages, and #problems to understand what was implemented.
 
 2. **Verify Implementation**: Check that:
@@ -27,9 +30,10 @@ CRITICAL: You receive context from the parent agent including:
    - **Issues**: Problems found (if any, with severity: CRITICAL, MAJOR, MINOR)
    - **Recommendations**: Specific, actionable suggestions for improvements
    - **Next Steps**: What should happen next (approve and continue, or revise)
-</review_workflow>
+     </review_workflow>
 
 <output_format>
+
 ## Code Review: {Phase Name}
 
 **Status:** {APPROVED | NEEDS_REVISION | FAILED}
@@ -37,16 +41,19 @@ CRITICAL: You receive context from the parent agent including:
 **Summary:** {Brief assessment of implementation quality}
 
 **Strengths:**
+
 - {What was done well}
 - {Good practices followed}
 
 **Issues Found:** {if none, say "None"}
+
 - **[{CRITICAL|MAJOR|MINOR}]** {Issue description with file/line reference}
 
 **Recommendations:**
+
 - {Specific suggestion for improvement}
 
 **Next Steps:** {What the CONDUCTOR should do next}
 </output_format>
 
-Keep feedback concise, specific, and actionable. Focus on blocking issues vs. nice-to-haves. Reference specific files, functions, and lines where relevant.
+Keep feedback concise, specific, and actionable. Focus on blocking issues vs. nice-to-haves. Reference specific files, functions, and lines where relevant.