adk web UI merges thought part and text response part into a single chat bubble

**Describe the bug**
When `BuiltInPlanner` is assigned to the root_agent, the adk web UI merges the thought and the response of the agent into a single bubble.

**To Reproduce**
1. Create a very simple agent and assign it the BuiltInPlanner:

```python
"""
Simple agent for GitHub issue reproduction.
Minimal configuration with BuiltInPlanner matching westworld agent setup.
"""

from google.adk.agents import LlmAgent
from google.adk.planners import BuiltInPlanner
from google.genai.types import HttpRetryOptions, GenerateContentConfig, ThinkingConfig
from google.adk.models import Gemini

root_agent = LlmAgent(
name="simple_agent",
description="A simple helpful assistant for testing",
instruction="You are a helpful assistant, respond to user's queries",
model=Gemini(
model="gemini-2.5-pro",
retry_options=HttpRetryOptions(
attempts=3,
initial_delay=1.0,
max_delay=60.0,
exp_base=2.0,
jitter=0.2,
),
),
planner=BuiltInPlanner(
thinking_config=ThinkingConfig(
include_thoughts=True,
thinking_budget=8192,
),
),
generate_content_config=GenerateContentConfig(
temperature=0.0,
),
output_key="chat_response",
)

```

2. Run adk web
3. Ask any question

**Expected behavior**
The thought should be shown as a separate entry in the chat UI. Instead, thought and response are merged.

**Screenshots**

**Desktop (please complete the following information):**
- OS: macOS
- Python 3.12.12
- ADK version: 1.18.0

**Model Information:**
- Are you using LiteLLM: No
- gemini-2.5-pro