refactor: restructure web application with modular JavaScript and remove legacy code

- Deleted the `app.js` file and migrated its functionality to a modular structure with multiple JavaScript files for better organization and maintainability.
- Updated `index.html` to reference the new `main.js` module, ensuring proper loading of the application.
- Introduced new utility modules for API requests, authentication, calendar handling, and DOM manipulation to enhance code clarity and separation of concerns.
- Enhanced CSS styles for improved layout and theming consistency across the application.
- Added comprehensive comments and documentation to new modules to facilitate future development and understanding.

webapp/js/dom.js

@@ -0,0 +1,43 @@
+/**
+ * DOM references and shared application state.
+ */
+
+/** @type {HTMLDivElement|null} */
+export const calendarEl = document.getElementById("calendar");
+
+/** @type {HTMLElement|null} */
+export const monthTitleEl = document.getElementById("monthTitle");
+
+/** @type {HTMLDivElement|null} */
+export const dutyListEl = document.getElementById("dutyList");
+
+/** @type {HTMLElement|null} */
+export const loadingEl = document.getElementById("loading");
+
+/** @type {HTMLElement|null} */
+export const errorEl = document.getElementById("error");
+
+/** @type {HTMLElement|null} */
+export const accessDeniedEl = document.getElementById("accessDenied");
+
+/** @type {HTMLElement|null} */
+export const headerEl = document.querySelector(".header");
+
+/** @type {HTMLElement|null} */
+export const weekdaysEl = document.querySelector(".weekdays");
+
+/** @type {HTMLButtonElement|null} */
+export const prevBtn = document.getElementById("prevMonth");
+
+/** @type {HTMLButtonElement|null} */
+export const nextBtn = document.getElementById("nextMonth");
+
+/** Currently viewed month (mutable). */
+export const state = {
+  /** @type {Date} */
+  current: new Date(),
+  /** @type {object[]} */
+  lastDutiesForList: [],
+  /** @type {ReturnType<typeof setInterval>|null} */
+  todayRefreshInterval: null
+};