feature: support configurable FastAPI root path

### Describe the feature

I want to be able to host vLLM under a subpath (e.g. example.com/vllm) instead of dedicating a whole subdomain.

### Why do you need this feature?

`vllm serve` supports configuring the FastAPI root path. The router should expose the same option so it can run under a subpath as well.

### Additional context

https://docs.vllm.ai/en/stable/cli/serve/#-root-path