feat: Support Claude Code CLI as alternative backend for AI supervision

[johnx25bd]

Summary

Allow VC to use Claude Code CLI (claude -p) instead of the Anthropic API SDK for AI supervision tasks, enabling users to run VC entirely through their existing Claude subscription without requiring a separate API key.

Motivation

The Problem

VC currently requires two separate billing relationships with Anthropic:

Layer	Billing Model	Used For
Coding Agent	Claude subscription (Pro/Max)	Code execution via claude CLI
AI Supervision	Anthropic API (pay-per-token)	Assessment, analysis, deduplication

This creates friction:

• Users must obtain and manage an ANTHROPIC_API_KEY
• API costs are in addition to subscription fees
• Variable billing makes costs unpredictable

The Opportunity

Claude Code's print mode (-p) now supports structured JSON output with schema validation:

claude -p \
  --output-format json \
  --json-schema '{"type":"object","properties":{...}}' \
  --tools "" \
  --model sonnet \
  "Your prompt here"

This provides everything VC's supervision layer needs, meaning all AI usage could flow through the user's existing subscription.

User Impact

Scenario	Current	Proposed
Max subscriber ($100/mo)	Pays subscription + API overage	All usage included
Pro subscriber ($20/mo)	Pays subscription + API overage	All usage included
Setup complexity	Requires API key configuration	Just claude login
Cost predictability	Variable (token-based)	Fixed monthly

Proposed Solution

Architecture

Introduce a pluggable AIBackend interface:

type AIBackend interface {
    Complete(ctx context.Context, prompt string, opts CompletionOptions) (string, error)
}

With two implementations:

1. AnthropicSDKBackend - existing behavior (API key)
2. ClaudeCodeBackend - new option (subscription)

Configuration

# Use Claude Code CLI (subscription billing)
vc execute --use-claude-code

# Use API key (current default)
vc execute

Or via environment:

export VC_AI_BACKEND=claude-code

Acceptance Criteria

• New AIBackend interface abstracts AI completion calls
• ClaudeCodeBackend implementation shells out to claude -p
• --use-claude-code flag added to vc execute
• VC runs without ANTHROPIC_API_KEY when using CLI backend
• All supervision operations work: assessment, analysis, deduplication, loop detection
• Graceful error handling when claude CLI unavailable
• Documentation updated with new configuration options

Trade-offs & Considerations

Advantages

• No API key required for subscribers
• Predictable monthly billing
• Simpler onboarding experience
• Single billing relationship

Limitations

• Subscription rate limits apply (Pro is limited; Max is generous)
• No token-level cost tracking (CLI doesn't expose usage)
• Slightly higher latency (process spawn vs HTTP connection reuse)
• Requires Claude Code CLI to be installed and authenticated

Mitigations

• Keep API backend as default for backwards compatibility
• Document rate limit considerations for Pro users
• Add clear error messages for CLI authentication issues

Additional Context

References

• Using Claude Code with Pro/Max plans
• API vs Subscription billing behavior

Files Likely Affected

• internal/ai/backend.go (new)
• internal/ai/supervisor.go
• internal/ai/assessment.go
• internal/ai/analysis.go
• internal/ai/deduplication.go
• cmd/vc/execute.go

Estimated Scope

Medium (~450 LOC, 2-3 days)

[johnx25bd]

This also could address #3