feat: sync room info in real time from system messages

[Khizarshah01]

Sync room information in real time in EmbeddedChat

Acceptance Criteria fulfillment

• Room information (topic, announcement, description, privacy) updates are reflected in real time
• Room Information sidebar updates without requiring a page refresh
• Chat header reflects updated room information automatically

Fixes #1119

Video/Screenshots

Screencast.from.2026-01-27.20-52-22.mp4

PR Test Details

Manual Testing

• Open EmbeddedChat and join a room
• Open the Room Information sidebar
• From another client (e.g., Rocket.Chat main app), update:
  • room topic
  • room announcement
  • room description
  • room privacy
• Verify the Room Information sidebar updates in real time
• Verify the chat header updates in real time
• Confirm no page refresh is required

Note: The PR will be ready for live testing at
https://rocketchat.github.io/EmbeddedChat/pulls/pr-<pr_number>
after approval. Contributors are requested to replace <pr_number> with the actual PR number.