fix: Asia/Seoul 타임존 지원을 위해 luxon 라이브러리 도입

- backend/routes/todos.js: 오늘의 할일 조회 시 KST 기준으로 날짜 계산
- backend/routes/schedules.js: 주간/월간 일정 조회 시 KST 기준으로 날짜 범위 계산
- backend/routes/bible.js: 오늘의 성경 구절 조회 시 KST 기준으로 날짜 계산
- flutter_app: Mock 데이터 사용 시 타임존 관련 주석 추가

backend/routes/schedules.js

@@ -1,31 +1,35 @@
 const express = require("express");
+const { DateTime } = require("luxon");
 const Schedule = require("../models/Schedule");
 
 const router = express.Router();
 
-const startOfWeek = (date = new Date()) => {
-  const copy = new Date(date);
-  const day = copy.getDay();
-  const diff = day === 0 ? -6 : 1 - day;
-  copy.setDate(copy.getDate() + diff);
-  copy.setHours(0, 0, 0, 0);
-  return copy;
+// Korea Standard Time zone
+const KST_TIMEZONE = "Asia/Seoul";
+
+const startOfWeek = () => {
+  // Get current time in KST and find the start of the week (Monday)
+  const nowKst = DateTime.now().setZone(KST_TIMEZONE);
+  // Luxon uses 1 = Monday, 7 = Sunday
+  const startOfWeekKst = nowKst.startOf("week"); // Monday 00:00:00.000
+  return startOfWeekKst.toJSDate();
 };
 
-const endOfWeek = (date = new Date()) => {
-  const start = startOfWeek(date);
-  const end = new Date(start);
-  end.setDate(end.getDate() + 6);
-  end.setHours(23, 59, 59, 999);
-  return end;
+const endOfWeek = () => {
+  // Get current time in KST and find the end of the week (Sunday)
+  const nowKst = DateTime.now().setZone(KST_TIMEZONE);
+  const endOfWeekKst = nowKst.endOf("week"); // Sunday 23:59:59.999
+  return endOfWeekKst.toJSDate();
 };
 
-const startOfMonth = (date = new Date()) => {
-  return new Date(date.getFullYear(), date.getMonth(), 1, 0, 0, 0, 0);
+const startOfMonth = () => {
+  const nowKst = DateTime.now().setZone(KST_TIMEZONE);
+  return nowKst.startOf("month").toJSDate();
 };
 
-const endOfMonth = (date = new Date()) => {
-  return new Date(date.getFullYear(), date.getMonth() + 1, 0, 23, 59, 59, 999);
+const endOfMonth = () => {
+  const nowKst = DateTime.now().setZone(KST_TIMEZONE);
+  return nowKst.endOf("month").toJSDate();
 };
 
 router.get("/", async (req, res) => {