Say I'm using Claude Code or GPT Codex's harnesses but also sending some queries to the respective Anthropic and OpenAI models via OpenRouter.

Do harnesses and therefore sending the queries directly to the LLM providers have caching and other benefits that OpenRouter does not provide? Would I get any of those benefits if I simply proxied any requests to the major providers' harnesses through OpenRouter? Or only if the requests go straight from the harness to the provider's API?