update template run.yaml to include openai api key for braintrust (#590)

# What does this PR do?

**Why**
- braintrust provider needs OpenAI API Key set in config for
DirectClient to work

## Test Plan
```
python llama_stack/scripts/distro_codegen.py 
```

<img width="340" alt="image"
src="https://github.com/user-attachments/assets/eae38296-f880-40f0-9a9e-46a12038db64">

- set API key in client via provider_data
<img width="907" alt="image"
src="https://github.com/user-attachments/assets/3d74cd7c-dc7e-4a42-8a40-c22f19b0c534">


## Before submitting

- [ ] This PR fixes a typo or improves the docs (you can dismiss the
other checks if that's the case).
- [ ] Ran pre-commit to handle lint / formatting issues.
- [ ] Read the [contributor
guideline](https://github.com/meta-llama/llama-stack/blob/main/CONTRIBUTING.md),
      Pull Request section?
- [ ] Updated relevant documentation.
- [ ] Wrote necessary unit or integration tests.

llama_stack/templates/bedrock/run.yaml

@@ -63,7 +63,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/fireworks/run.yaml

@@ -65,7 +65,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/hf-endpoint/run-with-safety.yaml

@@ -70,7 +70,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/hf-endpoint/run.yaml

@@ -65,7 +65,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/hf-serverless/run-with-safety.yaml

@@ -70,7 +70,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/hf-serverless/run.yaml

@@ -65,7 +65,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/meta-reference-gpu/run-with-safety.yaml

@@ -72,7 +72,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/meta-reference-gpu/run.yaml

@@ -66,7 +66,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/meta-reference-quantized-gpu/run.yaml

@@ -68,7 +68,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/ollama/run-with-safety.yaml

@@ -64,7 +64,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/ollama/run.yaml

@@ -64,7 +64,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/tgi/run-with-safety.yaml

@@ -68,7 +68,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/tgi/run.yaml

@@ -64,7 +64,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/together/run.yaml

@@ -65,7 +65,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite

llama_stack/templates/vllm-gpu/run.yaml

@@ -68,7 +68,8 @@ providers:
     config: {}
   - provider_id: braintrust
     provider_type: inline::braintrust
-    config: {}
+    config:
+      openai_api_key: ${env.OPENAI_API_KEY:}
 metadata_store:
   namespace: null
   type: sqlite