### Check for existing issues

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

### What happened?

An A2A agent registered on the proxy has authentication headers configured via the Admin UI under **Agents → Authentication Headers → Static Headers** (in my case `x-api-key`). The header is correctly persisted — it is returned by `GET /v1/agents` in the `static_headers` field.

When the agent is invoked through the **native A2A route** (`POST /a2a/{agent_id}`, JSON-RPC), LiteLLM correctly attaches the static header to upstream requests.

When the **same agent** is invoked through the documented OpenAI-compatible bridge — `model: "a2a/<agent-name>"` on `POST /v1/chat/completions` ([docs: Invoking A2A Agents](https://docs.litellm.ai/docs/a2a_invoking_agents)) — the static header is **never sent** to the backend agent, which rejects the request:

``` InternalServerError: Error code: 500 - {'error': {'message': 'litellm.APIConnectionError: A2aException - {"error":"Missing or invalid X-API-Key header.","code":"authentication_error"}', 'type': None, 'param': None, 'code': '500'}} ```

I also verified that neither of the other documented header mecha…