fix(openai): add missing stream parameter for Responses API

- The OpenAI Responses API actually requires the 'stream: true'
parameter in the JSON body, contrary to some documentation summaries.
- Omitting it caused the API to return a full application/json
response instead of SSE text/event-stream, leading to stream failures
and probe warnings in the proxy logs.

src/providers/openai.rs

@@ -664,7 +664,6 @@ impl super::Provider for OpenAIProvider {
         let mut body = serde_json::json!({
             "model": request.model,
             "input": input_parts,
-            "stream": true,
         });
 
         // Add standard parameters
@@ -711,6 +710,7 @@ impl super::Provider for OpenAIProvider {
             }
         }
 
+        body["stream"] = serde_json::json!(true);
         let url = format!("{}/responses", self.config.base_url);
         let api_key = self.api_key.clone();
         let model = request.model.clone();
@@ -889,16 +889,11 @@ impl super::Provider for OpenAIProvider {
                     Ok(_) => continue,
                     Err(e) => {
                          // Attempt to probe for the actual error body
-                        let mut probe_body_no_stream = probe_body.clone();
-                        if let Some(obj) = probe_body_no_stream.as_object_mut() {
-                            obj.remove("stream");
-                        }
-
                         let probe_resp = probe_client
                             .post(&url)
                             .header("Authorization", format!("Bearer {}", api_key))
                             .header("Accept", "application/json")
-                            .json(&probe_body_no_stream)
+                            .json(&probe_body)
                             .send()
                             .await;