Add unit and integration tests for garbage system

- Extract pure game logic functions to game-logic.js for testability
- Add Jest testing framework with 57 tests covering:
  * Unit tests for pure functions (createEmptyBoard, checkBoardOverflow, etc.)
  * Integration tests for garbage system (addGarbageToPlayer, sendGarbage)
  * Socket.io integration tests for multiplayer flow
- Refactor index.js to use extracted functions
- Tests verify garbage elimination bug fix: players only eliminated when board overflows

server/package.json

@@ -5,11 +5,17 @@
   "main": "index.js",
   "scripts": {
     "start": "node index.js",
-    "dev": "node index.js"
+    "dev": "node index.js",
+    "test": "jest",
+    "test:coverage": "jest --coverage"
   },
   "dependencies": {
     "express": "^4.18.2",
     "socket.io": "^4.7.2",
     "uuid": "^9.0.0"
+  },
+  "devDependencies": {
+    "jest": "^29.7.0",
+    "socket.io-client": "^4.8.3"
   }
 }