docs: Add notification inband mode for LiveObjects

[kaschula]

Summary

• Add documentation for the new notification inband mode for LiveObjects
• Reorganize the inband objects page to clearly distinguish between the two available modes
• Add JSON examples for Counter and Map object message formats as the REST API reference they previously linked to have been removed.

Changes

New notification mode documentation:

• Explains that notification mode sends a notification when an objects operation is received (not just when state changes)
• Documents the message format with the link property for fetching state via REST API
• Clarifies that no initial state is sent on attach
• Provides usage guidance on when to use each mode

Improved objects mode documentation:

• Reorganized existing content under a dedicated "Objects mode" section
• Added concrete JSON examples showing the message format for both Counter and Map objects

Updated mode comparison table:

• Added a comparison table at the top showing both objects and notification modes
• Updated enable section to show how to configure either mode

Checklist

• Commits have been rebased.
• Linting has been run against the changed file(s).
• The PR adheres to the writing style guide and contribution guide.

[coderabbitai]

Important

Review skipped

Auto reviews are disabled on this repository.

Please check the settings in the CodeRabbit UI or the .coderabbit.yaml file in this repository. To trigger a single review, invoke the @coderabbitai review command.

You can disable this status message by setting the reviews.review_status to false in the CodeRabbit configuration file.

• 🔍 Trigger a full review

---

Thanks for using CodeRabbit! It's free for OSS, and your support helps us grow. If you like it, consider giving us a shout-out.

❤️ Share

• X
• Mastodon
• Reddit
• LinkedIn

_{Comment @coderabbitai help to get the list of available commands and usage tips.}