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.

packages/infra/prisma/migrations/20260725000000_add_input_event/migration.sql

@@ -0,0 +1,25 @@
+CREATE TYPE "InputEventStatus" AS ENUM ('PENDING', 'PROCESSING', 'SUCCEEDED', 'FAILED');
+CREATE TYPE "InputEventTarget" AS ENUM ('API', 'ENGINE');
+
+CREATE TABLE "input_event" (
+    "sequence" BIGSERIAL NOT NULL,
+    "request_id" TEXT NOT NULL,
+    "target" "InputEventTarget" NOT NULL,
+    "event_type" TEXT NOT NULL,
+    "payload" JSONB NOT NULL DEFAULT '{}'::jsonb,
+    "actor_user_id" TEXT,
+    "status" "InputEventStatus" NOT NULL DEFAULT 'PENDING',
+    "result" JSONB,
+    "error" TEXT,
+    "attempts" INTEGER NOT NULL DEFAULT 0,
+    "locked_by" TEXT,
+    "lease_until" TIMESTAMP(3),
+    "created_at" TIMESTAMP(3) NOT NULL DEFAULT CURRENT_TIMESTAMP,
+    "processing_at" TIMESTAMP(3),
+    "completed_at" TIMESTAMP(3),
+
+    CONSTRAINT "input_event_pkey" PRIMARY KEY ("sequence")
+);
+
+CREATE UNIQUE INDEX "input_event_request_id_key" ON "input_event"("request_id");
+CREATE INDEX "input_event_target_status_sequence_idx" ON "input_event"("target", "status", "sequence");