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/planning-subagent.agent.md

@@ -4,6 +4,7 @@ argument-hint: Research goal or problem statement
 tools: ['search', 'usages', 'problems', 'changes', 'testFailure', 'fetch', 'githubRepo']
 # model: Claude Sonnet 4.5 (copilot)
 ---
+
 You are a PLANNING SUBAGENT called by a parent CONDUCTOR agent.
 
 Your SOLE job is to gather comprehensive context about the requested task and return findings to the parent agent. DO NOT write plans, implement code, or pause for user feedback.
@@ -28,20 +29,22 @@ Your SOLE job is to gather comprehensive context about the requested task and re
    - Note patterns, conventions, or constraints
    - Suggest 2-3 implementation approaches if multiple options exist
    - Flag any uncertainties or missing information
-</workflow>
+     </workflow>
 
 <research_guidelines>
+
 - Work autonomously without pausing for feedback
 - Prioritize breadth over depth initially, then drill down
 - Document file paths, function names, and line numbers
 - Note existing tests and testing patterns
 - Identify similar implementations in the codebase
 - Stop when you have actionable context, not 100% certainty
-</research_guidelines>
+  </research_guidelines>
 
 Return a structured summary with:
+
 - **Relevant Files:** List with brief descriptions
 - **Key Functions/Classes:** Names and locations
 - **Patterns/Conventions:** What the codebase follows
 - **Implementation Options:** 2-3 approaches if applicable
-- **Open Questions:** What remains unclear (if any)
+- **Open Questions:** What remains unclear (if any)