### Check for existing issues

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

### Context

Filing this at Krrish's request after a Discord thread. We run LiteLLM Proxy in production in front of Azure OpenAI deployments spread across several regions plus Bedrock, and we maintain a patched build of `litellm/integrations/prometheus.py` because the shipped exporter cannot answer the questions we need it to answer. This issue documents what we hit, what we changed, and which of those changes I think belong upstream. Happy to send each as a separate PR.

All line references are against `litellm_internal_staging` at `24123269ccb7`, since that is the default branch and where PRs land. The same lines are present on `main`.

cc @yucheng-berri, who owns most of the recent work in this file.

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### Problem 1: rate-limit gauges silently drop a value of `0`

`set_llm_deployment_success_metrics` guards both gauges with a truthy check:

```python # litellm/integrations/prometheus.py:2694 if remaining_requests: ... self.litellm_remaining_requests_metric.labels(**_labels).set(remaining_requests)

# litellm/integrations/prometheus.py:2708 if remain…