feat: implement input event system with durable command handling

- Introduced InputEvent model with status tracking (PENDING, PROCESSING, SUCCEEDED, FAILED) and unique request IDs.
- Added DatabaseTurnDaemonTransport for sending commands and handling idempotency.
- Implemented executeInputEvent function to manage input event lifecycle and error handling.
- Created DatabaseTurnDaemonCommandQueue for managing command processing and lease recovery.
- Enhanced turn daemon lifecycle to support atomic command execution and error recovery.
- Added tests for input event atomicity, command queuing, and error handling scenarios.

app/game-engine/src/index.ts

@@ -5,6 +5,7 @@ import { runTurnDaemonCli } from './turn/cli.js';
 
 export * from './lifecycle/types.js';
 export * from './lifecycle/clock.js';
+export * from './lifecycle/databaseCommandQueue.js';
 export * from './lifecycle/inMemoryControlQueue.js';
 export * from './lifecycle/turnDaemonLifecycle.js';
 export * from './lifecycle/getNextTickTime.js';