docs: Add 'Listing All Conversations' section with search endpoint

Documents the search endpoint with correct response format:
- Returns 'items' array (not 'results')
- Shows pagination with next_page_id

Co-authored-by: openhands <openhands@all-hands.dev>

Author: openhands-agent

openhands/usage/cloud/cloud-api.mdx

@@ -333,6 +333,58 @@ while True:
     time.sleep(30)
 ```
 
+### Listing All Conversations
+
+To list all your conversations, use the search endpoint:
+
+<Tabs>
+  <Tab title="cURL">
+    ```bash
+    curl -X GET "https://app.all-hands.dev/api/v1/app-conversations/search?limit=20" \
+      -H "Authorization: Bearer YOUR_API_KEY"
+    ```
+  </Tab>
+  <Tab title="Python (with requests)">
+    ```python
+    import requests
+
+    api_key = "YOUR_API_KEY"
+    headers = {"Authorization": f"Bearer {api_key}"}
+
+    response = requests.get(
+        "https://app.all-hands.dev/api/v1/app-conversations/search",
+        headers=headers,
+        params={"limit": 20}
+    )
+    result = response.json()
+
+    for conv in result.get("items", []):
+        print(f"ID: {conv['id']}, Status: {conv.get('execution_status')}")
+    ```
+  </Tab>
+</Tabs>
+
+**Response:**
+```json
+{
+  "items": [
+    {
+      "id": "660e8400-e29b-41d4-a716-446655440001",
+      "sandbox_status": "RUNNING",
+      "execution_status": "finished",
+      "selected_repository": "yourusername/your-repo",
+      "title": "Fix README"
+    }
+  ],
+  "next_page_id": null
+}
+```
+
+<Note>
+  The search endpoint returns conversations in the `items` array. Use `next_page_id` 
+  for pagination if you have more conversations than the `limit`.
+</Note>
+
 ## Rate Limits
 
 If you have too many conversations running at once, older conversations will be paused to limit the number of concurrent conversations.