[TEST]Update nightly cases and add mtpx (#4111)

### What this PR does / why we need it?
This PR updates some nightly test cases and adds mtpx cases, we need to
test them daily
### Does this PR introduce _any_ user-facing change?
No
### How was this patch tested?
By running the test

- vLLM version: v0.11.0
- vLLM main:
83f478bb19

---------

Signed-off-by: jiangyunfan1 <jiangyunfan1@h-partners.com>

tools/send_request.py

@@ -0,0 +1,23 @@
+from typing import Any
+
+import requests
+
+data: dict[str, Any] = {
+    "messages": [{
+        "role": "user",
+        "content": "",
+    }],
+}
+
+
+def send_text_request(prompt, model, server, request_args=None):
+    data["messages"][0]["content"] = prompt
+    data["model"] = model
+    url = server.url_for("v1", "chat", "completions")
+    if request_args:
+        data.update(request_args)
+    response = requests.post(url, json=data)
+    print("Status Code:", response.status_code)
+    response_json = response.json()
+    print("Response:", response_json)
+    assert response_json["choices"][0]["message"]["content"], "empty response"