Sniffs a real Claude Code request on startup to capture exact HTTP headers,
then replays them for all proxied requests. Injects the billing header with
per-request SHA256 fingerprint into the system prompt. Uses utls with Chrome
TLS fingerprint to pass Cloudflare's bot detection on api.anthropic.com.
Supports both streaming (SSE) and non-streaming modes, round-robin credential
selection with automatic failover, and loading OAuth tokens from both
cli-proxy-api auth files and native ~/.claude/.credentials.json.