refactor: share concurrency-limiting semaphore across model servers #1655

Context

While reviewing #1286, @cmunley1 noted that the per-process concurrency-limiting semaphore initialized in inference_provider/app.py is duplicated logic and could be reused/shared somewhere.

# responses_api_models/inference_provider/app.py
self._semaphore = Semaphore(self.config.num_concurrent_requests)

Problem

The same semaphore-init pattern is duplicated across multiple model servers:

• responses_api_models/inference_provider/app.py — Semaphore(self.config.num_concurrent_requests)
• responses_api_models/azure_openai_model/app.py — Semaphore(self.config.num_concurrent_requests) (identical)
• responses_api_models/openai_model/app.py — asyncio.Semaphore(max_concurrent_requests) with a nullcontext() fallback when unlimited

(Note: vllm_model does not currently use a semaphore at all — no num_concurrent_requests / _semaphore.)

The base classes SimpleResponsesAPIModel / BaseResponsesAPIModelConfig in nemo_gym/base_responses_api_model.py don't define num_concurrent_requests or a semaphore, so there's no shared home for this today.

Proposed change

Lift the concurrency-limit config field + semaphore init into the base model config/class so all model servers can share a single implementation, e.g.:

• Add an optional num_concurrent_requests (or max_concurrent_requests) field to BaseResponsesAPIModelConfig
• Initialize a self._semaphore (falling back to nullcontext() when unlimited) in the base model_post_init
• Migrate inference_provider, azure_openai_model, and openai_model to use it, reconciling the naming/default differences

Notes

• Out of scope for feat: add inference_provider server for hosted inference providers #1286 (which only adds the inference_provider server); tracking as a follow-up to avoid touching unrelated model servers in that PR.
• Should reconcile the differing field names (num_concurrent_requests vs max_concurrent_requests) and defaults (1000 vs None/unlimited) during the refactor.

Ref #1286