### Check for existing issues

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

### What happened?

### What happened

For OpenAI models that report **cache-write** tokens, LiteLLM does not price the cache-write portion of the request, and does not honor tiered/priced cache-creation keys. As a result the `response_cost` for any request that writes to the prompt cache is **understated**, and the error compounds across three separate places in the cost path:

1. **Cost function drops `cache_write_tokens`.** In `litellm/litellm_core_utils/llm_cost_calc/utils.py`, `_parse_prompt_tokens_details` only reads Anthropic-style `cache_creation_tokens` and ignores OpenAI's `cache_write_tokens` field. OpenAI reports cache writes under `prompt_tokens_details.cache_write_tokens` (chat) / `input_tokens_details.cache_write_tokens` (responses), so the cache-write token count arrives as `0` and those tokens are billed at the plain input rate (or not at all), instead of the 1.25× cache-write rate.

2. **Tiered cache-creation cost keys are not registered.** `get_model_info` copies a fixed set of cost keys onto `ModelInfo`, but omits `cache_creation_input_token_co…