Add unread notification badge

[wsxiaolin]

Motivation

• Show a red unread indicator on the footer notification icon when the authenticated user has unread messages or letters from Statistic.UnreadMessages / Statistic.UnreadLetters returned by a real login.
• Use a publish/subscribe approach so multiple UI pieces can react to unread-state changes.
• Clear the indicator when the notifications page is opened.

Description

• Add a small notification state helper src/services/notificationUnread.ts that exposes updateNotificationUnread, clearNotificationUnread, and hasUnreadNotifications and emits notificationUnreadChanged via the app Emitter when the unread state changes.
• Extend src/services/eventEmitter.ts to include a typed notificationUnreadChanged event.
• Update src/services/api/getData.ts login flow to call updateNotificationUnread for real logins (token/password or password login) using the Authenticate response Data.Statistic, avoiding updates for anonymous login(null, null).
• Subscribe the footer to the new unread state in src/components/utils/Footer.vue, rendering the red dot SVG circle (matching the requested appearance) when hasUnreadNotification is true.
• Clear the unread indicator when the notifications view is activated by calling clearNotificationUnread() in src/views/Notifications.vue.

Testing

• Ran the production build with npm run build (which runs vue-tsc and vite build), and the build completed successfully.

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Codex Task

[wsxiaolin]

@codex

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Can't wait for the next one!

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