### Check for existing issues

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

### The Feature

Implement a Dynamic Billing Reconciliation mechanism for OpenRouter provider to sync the response_cost with the actual billed amount.

Specifically, I propose adding a feature where LiteLLM can optionally fetch the final cost from OpenRouter's /api/v1/generation?id={id} endpoint after a request is completed, instead of solely relying on local static price maps. This is crucial for supporting OpenRouter's dynamic features like Service Tiers (Flex) and provider-specific discounts.

### Motivation, pitch

I am managing large-scale LLM infrastructure (Data Engineering at Digikala) and we use the /model/new endpoint to dynamically register hundreds of OpenRouter models.

**The Problem:** Currently, LiteLLM calculates costs locally based on static prices set at registration time. However, when we use extra_body={"service_tier": "flex"}, OpenRouter applies significant real-time discounts. Since LiteLLM is unaware of these dynamic billing changes, it logs the "standard" price in LiteLLM_SpendLogs, leading to a significant Cost Drift (e.g., LiteLLM logs $0…