[FEATURE]: /branch command to create new session with compacted context

[tobiastornros]

Feature hasn't been suggested before.

• I have verified this feature I'm about to request hasn't been suggested before.

Describe the enhancement you want to request

When working on larger tasks, I often want to explore different ideas or directions without losing the context of what I've already discussed.

A /branch command would create a new session with a summary of the current conversation, letting you branch off to try different approaches while preserving shared context.

Similar to git branches but for conversations.

Related to #4596 but with a different approach.

[github-actions]

This issue might be a duplicate of existing issues. Please check:

• [FEATURE]: Fork/Copy sessions with full context #4596: [FEATURE]: Fork/Copy sessions with full context - Similar feature request with the exact same approach of creating copies/branches of sessions
• Feature: generic /compact command, auto-compaction, and fork-aware conversations #4317: Feature: generic /compact command, auto-compaction, and fork-aware conversations - Proposes fork-aware conversation IDs and related infrastructure
• [FEATURE] Sliding window context management for long-running sessions #4659: [FEATURE] Sliding window context management for long-running sessions - Addresses context preservation and session management with related features

Feel free to ignore if none of these address your specific case.