Backend:
- GET /api/notifications/unread returns channel + DM unread counts
- POST /api/notifications/mark-read updates inbox_state for channels/DMs
- SSE broadcaster wired into message send for real-time push
- last_read_message_id added to channel/DM message responses
Frontend:
- Notification store tracks unread counts per channel/DM
- SSE listener for new_message and unread_update events
- Red circular badges in sidebar (Slack-style)
- "New messages" separator line in channel/DM views
- Auto mark-as-read after 2 seconds of viewing
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>