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/store/migrations/001_init.sql

@@ -0,0 +1,29 @@
+CREATE TABLE IF NOT EXISTS dag_runs (
+    id          TEXT PRIMARY KEY,
+    dag_name    TEXT NOT NULL,
+    dag_path    TEXT NOT NULL DEFAULT '',
+    status      TEXT NOT NULL DEFAULT 'pending' CHECK(status IN ('pending','running','success','failed','cancelled')),
+    trigger     TEXT NOT NULL DEFAULT 'manual' CHECK(trigger IN ('manual','cron','api')),
+    started_at  TEXT NOT NULL,
+    finished_at TEXT,
+    error       TEXT NOT NULL DEFAULT ''
+);
+
+CREATE TABLE IF NOT EXISTS dag_step_results (
+    id          TEXT PRIMARY KEY,
+    run_id      TEXT NOT NULL REFERENCES dag_runs(id) ON DELETE CASCADE,
+    step_name   TEXT NOT NULL,
+    status      TEXT NOT NULL DEFAULT 'pending' CHECK(status IN ('pending','running','success','failed','skipped')),
+    exit_code   INTEGER NOT NULL DEFAULT -1,
+    stdout      TEXT NOT NULL DEFAULT '',
+    stderr      TEXT NOT NULL DEFAULT '',
+    started_at  TEXT,
+    finished_at TEXT,
+    duration_ms INTEGER NOT NULL DEFAULT 0,
+    error       TEXT NOT NULL DEFAULT ''
+);
+
+CREATE INDEX IF NOT EXISTS idx_runs_dag_name ON dag_runs(dag_name);
+CREATE INDEX IF NOT EXISTS idx_runs_status ON dag_runs(status);
+CREATE INDEX IF NOT EXISTS idx_runs_started ON dag_runs(started_at DESC);
+CREATE INDEX IF NOT EXISTS idx_step_results_run ON dag_step_results(run_id);