feat(api): clarify default LLM model config selection logic

- Update API documentation to explicitly describe default configuration selection logic
- Add fallback behavior in repository to use first config when no default is marked
- Clarify difference between `/default` endpoint and `default_config` field
- Document that `default_config` is never null when configs list is not empty

docs/llm-model-configs-api.md

@@ -161,9 +161,14 @@ The `model_type` field accepts the following values:
 | Field | Type | Description |
 |-------|------|-------------|
 | `configs` | list[LLMModelConfigWithSource] | Effective configurations |
-| `default_config` | LLMModelConfigWithSource (nullable) | Default configuration |
+| `default_config` | LLMModelConfigWithSource (nullable) | Default configuration (never null if configs list is not empty) |
 | `total` | integer | Total count |
 
+**Default Configuration Selection Logic:**
+1. User's config marked with `is_default: true`
+2. Group's config marked with `is_default: true` (if user has no default)
+3. First config in the list (fallback if no default is marked)
+
 ### LLMModelConfigWithSource
 
 | Field | Type | Description |
@@ -368,6 +373,8 @@ curl -X GET http://localhost:3080/v3/access/users/{user_id}/llm-model-configs/de
   -H "Authorization: Bearer <token>"
 ```
 
+**Note:** This endpoint only returns configurations explicitly marked with `is_default: true`. If no configuration is marked as default, it returns 404.
+
 **Response:**
 ```json
 {
@@ -408,6 +415,12 @@ curl -X GET http://localhost:3080/v3/access/groups/{group_id}/llm-model-configs/
 
 The response format is the same as for users.
 
+---
+
+**Important Note:** This dedicated `/default` endpoint is different from the `default_config` field in the list response:
+- `/default` endpoint: Requires explicit `is_default: true` flag, returns 404 if not found
+- `default_config` field in list: Falls back to first config if no explicit default is marked
+
 ### 8. Delete a configuration
 
 ```bash