Add observability tracing for callback agent via Braintrust proxy

[fyang0507]

Problem

When the callback agent runs headless via sundial, there's no visibility into what it's doing — no trace of API calls, tool usage, latency, or token consumption. The only way to inspect a session today is to manually read the Claude session JSONL file after the fact.

Proposed solution: Braintrust AI proxy

Braintrust provides an AI proxy that intercepts LLM API calls, logs full request/response traces, and forwards to the provider. Claude Code respects ANTHROPIC_BASE_URL, so routing through Braintrust requires zero code changes — just environment variables.

Verified behavior

# Claude Code reads ANTHROPIC_BASE_URL
ANTHROPIC_BASE_URL=test claude -p "hi"
# → API Error: "test/v1/messages?beta=true" cannot be parsed as a URL.

Implementation (config-only)

callback_command: "ANTHROPIC_BASE_URL=https://braintrustproxy.com/v1 claude --dangerously-skip-permissions -p"

With BRAINTRUST_API_KEY either inline or in the shell profile (sundial runs commands via /bin/zsh -l -c, so login profile env vars are inherited).

What you get in Braintrust dashboard

• Full API request/response for every LLM call
• Tool call traces (what the agent read, what commands it ran)
• Token usage per turn
• Latency breakdown
• Session-level grouping

Alternatives considered

Approach	Pros	Cons
Braintrust proxy via ANTHROPIC_BASE_URL	Zero code changes, config-only, full API tracing	Requires Braintrust account, adds network hop
Claude Code hooks (--include-hook-events)	Built-in, no external service	Only lifecycle events (tool use, session start), not API-level traces
Post-hoc JSONL parsing	No dependencies	Manual, no dashboard, no real-time visibility
Claude Code plugin	Could be rich	No Braintrust plugin exists in official marketplace yet

Scope

This is a config/documentation change — document the Braintrust proxy pattern in the watch config comments and potentially in the skills docs. No code changes to outreach-cli needed.

Relationship

Complements #57 (cost analysis) — Braintrust would give real-time cost tracking per callback rather than manual JSONL parsing.