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/handlers_dags.go

@@ -0,0 +1,76 @@
+package main
+
+import (
+	"context"
+	"encoding/json"
+	"net/http"
+)
+
+func handleListDags(executor *Executor) http.HandlerFunc {
+	return func(w http.ResponseWriter, r *http.Request) {
+		dags, err := executor.ListDAGs()
+		if err != nil {
+			writeError(w, http.StatusInternalServerError, err.Error())
+			return
+		}
+		writeJSON(w, http.StatusOK, dags)
+	}
+}
+
+func handleGetDag(executor *Executor) http.HandlerFunc {
+	return func(w http.ResponseWriter, r *http.Request) {
+		name := r.PathValue("name")
+		info, dag, validation, err := executor.GetDAG(name)
+		if err != nil {
+			writeError(w, http.StatusNotFound, err.Error())
+			return
+		}
+
+		// Get recent runs.
+		runs, _, _ := executor.store.ListRuns(dag.Name, 10, 0)
+
+		resp := map[string]interface{}{
+			"info":       info,
+			"dag":        dag,
+			"validation": validation,
+			"runs":       runs,
+		}
+		writeJSON(w, http.StatusOK, resp)
+	}
+}
+
+func handleRunDag(executor *Executor) http.HandlerFunc {
+	return func(w http.ResponseWriter, r *http.Request) {
+		name := r.PathValue("name")
+		info, _, _, err := executor.GetDAG(name)
+		if err != nil {
+			writeError(w, http.StatusNotFound, err.Error())
+			return
+		}
+
+		// Execute asynchronously.
+		go func() {
+			ctx := context.Background()
+			executor.ExecuteDAG(ctx, info.FilePath, "api")
+		}()
+
+		// Return run acknowledgment.
+		writeJSON(w, http.StatusAccepted, map[string]string{
+			"status":  "accepted",
+			"dag":     name,
+			"message": "DAG execution started",
+		})
+	}
+}
+
+// --- JSON helpers ---
+
+func writeJSON(w http.ResponseWriter, status int, data interface{}) {
+	w.Header().Set("Content-Type", "application/json")
+	w.WriteHeader(status)
+	json.NewEncoder(w).Encode(data)
+}
+
+func writeError(w http.ResponseWriter, status int, msg string) {
+	writeJSON(w, status, map[string]string{"error": msg})
+}