feat(openai): Add verbosity parameter support for GPT-5 family models (#16660)

OpenAI's GPT-5 model family supports a verbosity parameter to control
the length and detail of responses. This parameter accepts three values:
'low', 'medium', or 'high'.

Changes:
- Added verbosity parameter to completion() and acompletion() signatures
- Added verbosity to DEFAULT_CHAT_COMPLETION_PARAM_VALUES in constants.py
- Added verbosity to get_optional_params() in utils.py
- Added verbosity to GPT-5 supported params list
- Updated OpenAI docs with verbosity usage examples
- Added comprehensive test for verbosity parameter

Supported models: gpt-5, gpt-5.1, gpt-5-mini, gpt-5-nano, gpt-5-codex, gpt-5-pro

docs/my-website/docs/providers/openai.md

@@ -486,6 +486,53 @@ curl -X POST 'http://0.0.0.0:4000/chat/completions' \
 
 See [OpenAI Reasoning documentation](https://platform.openai.com/docs/guides/reasoning) for more details on organization verification requirements.
 
+### Verbosity Control for GPT-5 Models
+
+The `verbosity` parameter controls the length and detail of responses from GPT-5 family models. It accepts three values: `"low"`, `"medium"`, or `"high"`.
+
+**Supported models:** All GPT-5 family models (`gpt-5`, `gpt-5.1`, `gpt-5-mini`, `gpt-5-nano`, `gpt-5-codex`, `gpt-5-pro`)
+
+**Use cases:**
+- **`"low"`**: Best for concise answers or simple code generation (e.g., SQL queries)
+- **`"medium"`**: Default - balanced output length
+- **`"high"`**: Use when you need thorough explanations or extensive code refactoring
+
+<Tabs>
+<TabItem value="sdk" label="SDK">
+```python
+import litellm
+
+# Low verbosity - concise responses
+response = litellm.completion(
+    model="gpt-5.1",
+    messages=[{"role": "user", "content": "Write a function to reverse a string"}],
+    verbosity="low"
+)
+
+# High verbosity - detailed responses
+response = litellm.completion(
+    model="gpt-5.1",
+    messages=[{"role": "user", "content": "Explain how neural networks work"}],
+    verbosity="high"
+)
+```
+</TabItem>
+
+<TabItem value="proxy" label="PROXY">
+```bash
+curl -X POST 'http://0.0.0.0:4000/chat/completions' \
+-H 'Content-Type: application/json' \
+-H 'Authorization: Bearer sk-1234' \
+-d '{
+    "model": "gpt-5.1",
+    "messages": [{"role": "user", "content": "Write a function to reverse a string"}],
+    "verbosity": "low"
+}'
+```
+</TabItem>
+</Tabs>
+
+
 ## OpenAI Chat Completion to Responses API Bridge
 
 Call any Responses API model from OpenAI's `/chat/completions` endpoint.