Each call through BudgetedClient emits llm.call: seconds, input,
output and cached tokens, and the answering model when a fallback
answered; a failed call logs how long it ran before it failed.
Usage now carries the server's cached-prompt count on both routes.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01J5Utyfzw7gF7UhjRDEtjTk