[FEATURE] Persist btw skill conversations and make them accessible in session history

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When I use the btw skill to spawn a separate session, the generated conversation
is lost after closing the window. There's no way to retrieve those previous btw conversations
once the session is closed.

Why This Matters

• I want to review decisions/discussions/brain-storming from btw sessions without having to re-spawn them
• Better continuity when working on related tasks
• Easier to compare different btw explorations

Proposed Solution

• btw skill conversations should be persisted (similar to regular session history)
• There should be a way to access/review previous btw conversations from within the main session
• Maybe a sidebar panel or a command like /btw-history to list past btw sessions

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

Interactive mode (TUI)

Use Case Example

_No response_

Additional Context

_No response_