[FEATURE] BTW mode conversations should be visible to the main conversation context

Problem

BTW mode is great for quick side questions during complex tasks, but its conversations are completely ephemeral — they're not accessible to the main conversation context after dismissal. This creates a practical issue:

• Important context discovered in BTW (like configuration problems, architectural decisions, or corrections to behavior) is silently lost
• The main agent cannot access or reference what was discussed in BTW
• Users must manually re-explain things from BTW to the main conversation, which defeats the purpose of a quick side channel
• There's no hook event to capture BTW exchanges, so even custom logging solutions can't preserve them

Use Case

During a coding session, I asked a BTW question about why I was being prompted for MCP tool permissions. The BTW agent explained the cause and suggested a fix. But when I returned to the main conversation, the main agent had no knowledge of this — I had to re-explain the issue and show a screenshot of the BTW exchange.

Proposed Solutions

Any of these would help (in order of preference):

1. Inject BTW context into the main conversation

After a BTW exchange is dismissed, append a compact summary as a system message visible to the main agent. Something like:

[BTW sidebar] User asked: "why am I getting MCP permission prompts?"
Response: MCP tools need to be added to the allow list in settings.local.json

This is the most seamless option — no user action needed, the main agent just knows.

2. Add a PostBTW hook event

Allow hooks to capture BTW exchanges. The hook would receive the user's question and the agent's response, enabling custom logging (e.g., session loggers that already exist for other hook events).

3. Write BTW exchanges to a session-scoped file

Store BTW Q&A pairs in a file (e.g., ~/.claude/btw-log-<session_id>.jsonl) that the main agent can read when relevant.

Current Workaround

Tell the main agent "remember: [thing from BTW]" — but this requires the user to manually relay information, which is exactly the friction BTW mode is supposed to eliminate.

Environment

• macOS, Claude Code CLI
• Max plan