chore: notify messages on emails incoming and outgoing (#30925)

apps/meteor/server/features/EmailInbox/EmailInbox_Incoming.ts

+import { api } from '@rocket.chat/core-services';
 import type {
 	ILivechatVisitor,
 	IOmnichannelRoom,
@@ -16,6 +17,7 @@ import { Livechat as LivechatTyped } from '../../../app/livechat/server/lib/Live
 import { QueueManager } from '../../../app/livechat/server/lib/QueueManager';
 import { settings } from '../../../app/settings/server';
 import { i18n } from '../../lib/i18n';
+import { broadcastMessageSentEvent } from '../../modules/watchers/lib/messages';
 import { logger } from './logger';
 
 type FileAttachment = VideoAttachmentProps & ImageAttachmentProps & AudioAttachmentProps;
@@ -236,6 +238,10 @@ export async function onEmailReceived(email: ParsedMail, inbox: string, departme
 				},
 			);
 			room && (await LivechatRooms.updateEmailThreadByRoomId(room._id, thread));
+			void broadcastMessageSentEvent({
+				id: msgId,
+				broadcastCallback: (message) => api.broadcast('message.sent', message),
+			});
 		})
 		.catch((err) => {
 			logger.error({

apps/meteor/server/features/EmailInbox/EmailInbox_Outgoing.ts

+import { api } from '@rocket.chat/core-services';
 import { isIMessageInbox } from '@rocket.chat/core-typings';
 import type { IEmailInbox, IUser, IMessage, IOmnichannelRoom, SlashCommandCallbackParams } from '@rocket.chat/core-typings';
 import { Messages, Uploads, LivechatRooms, Rooms, Users } from '@rocket.chat/models';
@@ -10,6 +11,7 @@ import { settings } from '../../../app/settings/server';
 import { slashCommands } from '../../../app/utils/server/slashCommand';
 import { callbacks } from '../../../lib/callbacks';
 import { i18n } from '../../lib/i18n';
+import { broadcastMessageSentEvent } from '../../modules/watchers/lib/messages';
 import { inboxes } from './EmailInbox';
 import type { Inbox } from './EmailInbox';
 import { logger } from './logger';
@@ -170,6 +172,10 @@ slashCommands.add({
 				},
 			},
 		);
+		void broadcastMessageSentEvent({
+			id: message._id,
+			broadcastCallback: (message) => api.broadcast('message.sent', message),
+		});
 
 		return sendSuccessReplyMessage({
 			msgId: message._id,