fix: strip prefix id from model name in /responses endpoint (#28575)

The /openai/responses endpoint forwarded the prefixed model id (e.g.
"myprovider.gpt-4o") to the upstream provider instead of the stripped
native name, causing "model not found" errors when a connection has a
Prefix ID configured.

generate_chat_completion() already strips the prefix before forwarding;
apply the same strip_provider_model_prefix() call in responses() after
the urlIdx routing (which needs the prefixed id) and re-serialize the
body afterwards.

Also fixes the Azure non-v1 deployment path, which built the deployment
URL from the prefixed model name.

Co-authored-by: Claude <noreply@anthropic.com>

backend/open_webui/routers/openai.py

@@ -1847,8 +1847,6 @@ async def responses(
     # Enforce per-model access control
     await check_model_access(user, await Models.get_model_by_id(model_id), BYPASS_MODEL_ACCESS_CONTROL)
 
-    body = JSONCodec.dumps(payload)
-
     if model_id:
         models = request.app.state.OPENAI_MODELS
         if not models or model_id not in models:
@@ -1859,6 +1857,9 @@ async def responses(
 
     url, key, api_config = await get_openai_connection(idx)
 
+    payload['model'] = strip_provider_model_prefix(payload['model'], api_config.get('prefix_id'))
+    body = JSONCodec.dumps(payload)
+
     r = None
     streaming = False