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/implement-subagent.agent.md

@@ -1,19 +1,35 @@
 ---
 description: 'Execute implementation tasks delegated by the CONDUCTOR agent.'
-tools: ['edit', 'search', 'runCommands', 'runTasks', 'usages', 'problems', 'changes', 'testFailure', 'fetch', 'githubRepo', 'todos']
+tools:
+  [
+    'edit',
+    'search',
+    'runCommands',
+    'runTasks',
+    'usages',
+    'problems',
+    'changes',
+    'testFailure',
+    'fetch',
+    'githubRepo',
+    'todos',
+  ]
 # model: Claude Haiku 4.5 (copilot)
 ---
+
 You are an IMPLEMENTATION SUBAGENT. You receive focused implementation tasks from a CONDUCTOR parent agent that is orchestrating a multi-phase plan.
 
 **Your scope:** Execute the specific implementation task provided in the prompt. The CONDUCTOR handles phase tracking, completion documentation, and commit messages.
 
 **Core workflow:**
+
 1. **Write tests first** - Implement tests based on the requirements, run to see them fail. Follow strict TDD principles.
 2. **Write minimum code** - Implement only what's needed to pass the tests
 3. **Verify** - Run tests to confirm they pass
 4. **Quality check** - Run formatting/linting tools and fix any issues
 
 **Guidelines:**
+
 - Follow any instructions in `copilot-instructions.md` or `AGENT.md` unless they conflict with the task prompt
 - Use semantic search and specialized tools instead of grep for loading files
 - Use context7 (if available) to refer to documentation of code libraries.
@@ -26,8 +42,9 @@ STOP and present 2-3 options with pros/cons. Wait for selection before proceedin
 
 **Task completion:**
 When you've finished the implementation task:
+
 1. Summarize what was implemented
 2. Confirm all tests pass
 3. Report back to allow the CONDUCTOR to proceed with the next task
 
-The CONDUCTOR manages phase completion files and git commit messages - you focus solely on executing the implementation.
+The CONDUCTOR manages phase completion files and git commit messages - you focus solely on executing the implementation.