### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

Closely related but distinct: - #27763 (**closed, completed**) — the mirror-image defect: Anthropic-native `cache_read_input_tokens` not normalized into `prompt_tokens_details.cached_tokens` for Vertex/Bedrock on `/v1/messages`. Same end symptom ("cache reads billed as full-priced input tokens"), opposite direction of translation. This report is the **OpenAI-backed** path, which was not covered by that fix. - #11364 (`cached_tokens` not populated, Anthropic direct), #11789 (Anthropic streaming cost tracking ignores cache reads), #7790 (async logging callbacks drop cache fields when streaming).

### What happened?

When `/v1/messages` is routed to an OpenAI model (i.e. the Responses-API bridge, `_should_route_to_responses_api()` → `LiteLLMMessagesToResponsesAPIHandler` → `AnthropicResponsesStreamWrapper`), **cache-read tokens are always reported as 0**, even when OpenAI returns a large `cached_tokens` count.

Consequences:

1. The `message_delta` usage returned to the client omits `cache_read_input_tokens` entirely, so Anthropic-format clients (e.g. anything speaki…