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/middleware.go

@@ -0,0 +1,30 @@
+package main
+
+import (
+	"log"
+	"net/http"
+	"time"
+)
+
+// corsMiddleware adds permissive CORS headers for development.
+func corsMiddleware(next http.Handler) http.Handler {
+	return http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		w.Header().Set("Access-Control-Allow-Origin", "*")
+		w.Header().Set("Access-Control-Allow-Methods", "GET, POST, PUT, DELETE, OPTIONS")
+		w.Header().Set("Access-Control-Allow-Headers", "Content-Type, Authorization")
+		if r.Method == http.MethodOptions {
+			w.WriteHeader(http.StatusNoContent)
+			return
+		}
+		next.ServeHTTP(w, r)
+	})
+}
+
+// loggingMiddleware logs each HTTP request with method, path and duration.
+func loggingMiddleware(next http.Handler) http.Handler {
+	return http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		start := time.Now()
+		next.ServeHTTP(w, r)
+		log.Printf("%s %s %s", r.Method, r.URL.Path, time.Since(start).Round(time.Millisecond))
+	})
+}