feat: prompt cache-aware routing — prefer providers with warm caches

[kianwoon]

Problem

The proxy already does raw body passthrough to preserve upstream prompt caching, but routing is static (weight-based). Two providers serving the same model may have very different cache hit rates, but traffic doesn't favor the one with the warmer cache.

Proposal

Track per-provider cache hit/miss signals from response headers (e.g., Anthropic's x-cache-hit, token usage cache_read_input_tokens) and use this to influence routing:

1. Record cache hit rates per (provider, model) pair
2. When multiple providers can serve a request, boost routing weight for the provider with higher cache hit rate
3. This directly reduces input token costs and latency

Expected Benefit

• Lower latency on cache hits (no re-processing of cached prefix)
• Reduced token costs (cache reads are cheaper)
• Smarter traffic distribution without manual weight tuning

Related

Part of stability & performance exploration vs direct Claude Code CLI → LLM gateway connections.