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-api/test/idempotentTransport.test.ts

@@ -0,0 +1,22 @@
+import { describe, expect, it } from 'vitest';
+
+import { IdempotentTurnDaemonTransport } from '../src/daemon/idempotentTransport.js';
+import { InMemoryTurnDaemonTransport } from '../src/daemon/inMemoryTransport.js';
+
+describe('IdempotentTurnDaemonTransport', () => {
+    it('derives stable ordered engine request IDs from the API input event', async () => {
+        const inner = new InMemoryTurnDaemonTransport();
+        const firstAttempt = new IdempotentTurnDaemonTransport(inner, 'api-event');
+        const retry = new IdempotentTurnDaemonTransport(inner, 'api-event');
+
+        await firstAttempt.sendCommand({ type: 'vacation', generalId: 7 });
+        await firstAttempt.sendCommand({ type: 'dropItem', generalId: 7, itemType: 'weapon' });
+        await retry.sendCommand({ type: 'vacation', generalId: 7 });
+
+        expect(inner.commands.map((entry) => entry.requestId)).toEqual([
+            'api-event:engine:0:vacation',
+            'api-event:engine:1:dropItem',
+            'api-event:engine:0:vacation',
+        ]);
+    });
+});