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/src/daemon/idempotentTransport.ts

@@ -0,0 +1,28 @@
+import type { TurnDaemonTransport } from './transport.js';
+import type { TurnDaemonCommand, TurnDaemonCommandResult, TurnDaemonStatus } from './types.js';
+
+export class IdempotentTurnDaemonTransport implements TurnDaemonTransport {
+    private sequence = 0;
+
+    constructor(
+        private readonly transport: TurnDaemonTransport,
+        private readonly parentRequestId: string
+    ) {}
+
+    async sendCommand(command: TurnDaemonCommand): Promise<string> {
+        return this.transport.sendCommand(this.scope(command));
+    }
+
+    async requestCommand(command: TurnDaemonCommand, timeoutMs?: number): Promise<TurnDaemonCommandResult | null> {
+        return this.transport.requestCommand(this.scope(command), timeoutMs);
+    }
+
+    async requestStatus(timeoutMs?: number): Promise<TurnDaemonStatus | null> {
+        return this.transport.requestStatus(timeoutMs);
+    }
+
+    private scope(command: TurnDaemonCommand): TurnDaemonCommand {
+        const requestId = `${this.parentRequestId}:engine:${this.sequence++}:${command.type}`;
+        return { ...command, requestId } as TurnDaemonCommand;
+    }
+}