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_runs.go

@@ -0,0 +1,59 @@
+package main
+
+import (
+	"net/http"
+	"strconv"
+)
+
+func handleListRuns(executor *Executor) http.HandlerFunc {
+	return func(w http.ResponseWriter, r *http.Request) {
+		dagName := r.URL.Query().Get("dag")
+		limit, _ := strconv.Atoi(r.URL.Query().Get("limit"))
+		offset, _ := strconv.Atoi(r.URL.Query().Get("offset"))
+		if limit <= 0 || limit > 100 {
+			limit = 20
+		}
+		if offset < 0 {
+			offset = 0
+		}
+
+		runs, total, err := executor.store.ListRuns(dagName, limit, offset)
+		if err != nil {
+			writeError(w, http.StatusInternalServerError, err.Error())
+			return
+		}
+
+		writeJSON(w, http.StatusOK, map[string]interface{}{
+			"runs":   runs,
+			"total":  total,
+			"limit":  limit,
+			"offset": offset,
+		})
+	}
+}
+
+func handleGetRun(executor *Executor) http.HandlerFunc {
+	return func(w http.ResponseWriter, r *http.Request) {
+		id := r.PathValue("id")
+		run, err := executor.store.GetRun(id)
+		if err != nil {
+			writeError(w, http.StatusInternalServerError, err.Error())
+			return
+		}
+		if run == nil {
+			writeError(w, http.StatusNotFound, "run not found")
+			return
+		}
+
+		steps, err := executor.store.ListStepResults(id)
+		if err != nil {
+			writeError(w, http.StatusInternalServerError, err.Error())
+			return
+		}
+
+		writeJSON(w, http.StatusOK, map[string]interface{}{
+			"run":   run,
+			"steps": steps,
+		})
+	}
+}