feat: enhance duty information handling with contact details and current duty view

- Added `bot_username` to settings for dynamic retrieval of the bot's username.
- Implemented `_resolve_bot_username` function to fetch the bot's username if not set, improving user experience in group chats.
- Updated `DutyWithUser` schema to include optional `phone` and `username` fields for enhanced duty information.
- Enhanced API responses to include contact details for users, ensuring better communication.
- Introduced a new current duty view in the web app, displaying active duty information along with contact options.
- Updated CSS styles for better presentation of contact information in duty cards.
- Added unit tests to verify the inclusion of contact details in API responses and the functionality of the current duty view.

webapp/js/dom.js

@@ -32,6 +32,9 @@ export const prevBtn = document.getElementById("prevMonth");
 /** @type {HTMLButtonElement|null} */
 export const nextBtn = document.getElementById("nextMonth");
 
+/** @type {HTMLDivElement|null} */
+export const currentDutyViewEl = document.getElementById("currentDutyView");
+
 /** Currently viewed month (mutable). */
 export const state = {
   /** @type {Date} */