feat: implement real-time unread badges, presence tracking, and chat seen status

[trtajim]

Summary of Changes

• User Activity & Seen Schema: Added migrations for notifications_last_seen_at, chat_last_seen_at, and last_active_at columns on the users table.
• Unread Badge Synchronization: Shared accurate unread_notifications_count and unread_chat_count in HandleInertiaRequests and updated Navigation.tsx to show unread badges on desktop and mobile.
• Presence Channel Metadata: Updated broadcast channel authorizations in routes/channels.php to return image_url and is_verified for online users.
• Live Chat UX Improvements: Implemented auto mark-seen on chat view, presence sidebar with user avatars and verification badges, and responsive layout polish.

Summary by CodeRabbit

• New Features
  • Chat navigation now displays unread-message badges, with counts above nine shown as “9+”.
  • The online-member count opens a list of active members with profile details and links to their profiles.
  • Presence information now reflects whether a member was active within the last five minutes.
• Improvements
  • Notification pages show 10 items at a time. Opening the notification menu clears its unread indicator.
  • Unread notification and chat counts reflect activity since you last viewed each section.

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📥 Commits

Reviewing files that changed from the base of the PR and between a0beb56 and 511b5fd.

📒 Files selected for processing (11)

• app/Http/Controllers/ChatController.php
• app/Http/Controllers/NotificationController.php
• app/Http/Middleware/HandleInertiaRequests.php
• app/Models/User.php
• database/migrations/2026_10_05_080443_add_notifications_last_seen_at_to_users_table.php
• database/migrations/2026_10_05_174110_add_chat_last_seen_at_to_users_table.php
• database/migrations/2026_10_05_190800_add_last_active_at_to_users_table.php
• resources/js/components/NotificationDropdown.vue
• resources/js/components/navigation/Navigation.tsx
• resources/js/pages/Chat/Index.vue
• routes/channels.php

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