feat: add dag_engine app — CLI + web frontend for DAG execution (0007e)

Full DAG engine app with CLI subcommands (run, list, status, validate, server)
and React/Mantine web frontend. Uses net/http + embedded Vite build. SQLite
store for run history. Scheduler with cron_ticker for automated execution.
Compatible with existing dagu YAML format.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/dag_engine/frontend/src/api.ts

@@ -0,0 +1,63 @@
+import type {
+  DagSummary,
+  DagDetail,
+  DagRun,
+  RunDetail,
+  SchedulerStatus,
+} from "./types";
+
+const BASE = "/api";
+
+async function fetchJSON<T>(path: string, init?: RequestInit): Promise<T> {
+  const res = await fetch(`${BASE}${path}`, init);
+  if (!res.ok) {
+    const err = await res.json().catch(() => ({ error: res.statusText }));
+    throw new Error(err.error || res.statusText);
+  }
+  return res.json();
+}
+
+export function listDags(): Promise<DagSummary[]> {
+  return fetchJSON("/dags");
+}
+
+export function getDag(name: string): Promise<DagDetail> {
+  return fetchJSON(`/dags/${encodeURIComponent(name)}`);
+}
+
+export function triggerDag(
+  name: string
+): Promise<{ status: string; dag: string; message: string }> {
+  return fetchJSON(`/dags/${encodeURIComponent(name)}/run`, {
+    method: "POST",
+  });
+}
+
+export function listRuns(params?: {
+  dag?: string;
+  limit?: number;
+  offset?: number;
+}): Promise<{ runs: DagRun[]; total: number }> {
+  const search = new URLSearchParams();
+  if (params?.dag) search.set("dag", params.dag);
+  if (params?.limit) search.set("limit", String(params.limit));
+  if (params?.offset) search.set("offset", String(params.offset));
+  const qs = search.toString();
+  return fetchJSON(`/runs${qs ? "?" + qs : ""}`);
+}
+
+export function getRun(id: string): Promise<RunDetail> {
+  return fetchJSON(`/runs/${encodeURIComponent(id)}`);
+}
+
+export function startScheduler(): Promise<void> {
+  return fetchJSON("/scheduler/start", { method: "POST" });
+}
+
+export function stopScheduler(): Promise<void> {
+  return fetchJSON("/scheduler/stop", { method: "POST" });
+}
+
+export function getSchedulerStatus(): Promise<SchedulerStatus> {
+  return fetchJSON("/scheduler/status");
+}