### Check for existing issues

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

### The Feature

I would like LiteLLM Proxy to support an optional asynchronous priority queue mode.

The goal is to allow requests to be queued and scheduled based on business priority when upstream quota or capacity is scarce.

Suggested behavior:

1. Requests can be enqueued instead of immediately forwarded. 2. Queue items include model, key, team, user, priority, metadata, and enqueue time. 3. Worker processes claim queued requests and forward them to LiteLLM. 4. Queue ordering can consider request priority, team priority, and enqueue time. 5. Batch or low-priority workloads can be delayed when resources are constrained. 6. Admin UI/API can show queue depth, status, and failed items.

This should be optional and disabled by default so current synchronous proxy behavior remains unchanged.

### Motivation, pitch

LiteLLM is commonly used as a real-time gateway, but enterprise deployments sometimes need to handle scarce model quota or limited upstream capacity.

In those cases, not all traffic has equal priority:

- interactive applications should be served befor…