refactor: move database initialization from entrypoint to application

Move database initialization logic from shell script to Python application
lifespan, following separation of concerns and improving maintainability.

Benefits:
- Single source of truth for database initialization (api/main.py lifespan)
- Better testability - Python code vs shell scripts
- Clearer logging with structured messages
- Easier to debug and maintain
- Infrastructure (entrypoint.sh) focuses on service orchestration
- Application (api/main.py) owns its data layer

Changes:
- Removed database init from entrypoint.sh
- Enhanced lifespan function with detailed logging
- Simplified entrypoint script (now 4 steps instead of 5)
- All tests pass (28/28 API endpoint tests)

api/main.py

@@ -135,19 +135,27 @@ def create_app(
         from api.database import initialize_dev_database, initialize_database
 
         # Startup - use closure to access db_path from create_app scope
+        logger.info("🚀 FastAPI application starting...")
+        logger.info("📊 Initializing database...")
+
         if is_dev_mode():
             # Initialize dev database (reset unless PRESERVE_DEV_DATA=true)
+            logger.info("  🔧 DEV mode detected - initializing dev database")
             dev_db_path = get_db_path(db_path)
             initialize_dev_database(dev_db_path)
             log_dev_mode_startup_warning()
         else:
             # Ensure production database schema exists
+            logger.info("  🏭 PROD mode - ensuring database schema exists")
             initialize_database(db_path)
 
+        logger.info("✅ Database initialized")
+        logger.info("🌐 API server ready to accept requests")
+
         yield
 
         # Shutdown (if needed in future)
-        pass
+        logger.info("🛑 FastAPI application shutting down...")
 
     app = FastAPI(
         title="AI-Trader Simulation API",