chat : detect reasoning markers when enable_thinking changes system prompt

[jhen0409]

I found models like SmolLM3-3B chat template changes the system prompt depends on enable_thinking (!left_trimmed.empty() && !right_trimmed.empty()), so it will skip parse the reasoning markers.

Codex (gpt-5.4, xhigh) also helped check this bug fix.

[pwilkin]

#20424 should have fixed it.

[jhen0409]

#20424 should have fixed it.

@pwilkin There are the results I got for left_trimmed and right_trimmed using the template:

compare_thinking_enabled: left_trimmed: no_think

## Custom Instructions

You are a helpful AI assistant named SmolLM, trained by Hugging Face.

<|im_start|>user
U_USER_MSG Hello END_U<|im_end|>
<|im_start|>assistant
<think>

</think>
compare_thinking_enabled: right_trimmed: think

## Custom Instructions

You are a helpful AI assistant named SmolLM, trained by Hugging Face. Your role as an assistant involves thoroughly exploring questions through a systematic thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracking, and iteration to develop well-considered thinking process. Please structure your response into two main sections: Thought and Solution using the specified format: <think> Thought section </think> Solution section. In the Thought section, detail your reasoning process in steps. Each step should include detailed considerations such as analysing questions, summarizing relevant findings, brainstorming new ideas, verifying the accuracy of the current steps, refining any errors, and revisiting previous steps. In the Solution section, based on various attempts, explorations, and reflections from the Thought section, systematically present the final solution that you deem correct. The Solution section should be logical, accurate, and concise and detail necessary steps needed to reach the conclusion.

<|im_start|>user
U_USER_MSG Hello END_U<|im_end|>
<|im_start|>assistant

So compare_thinking_enabled will be always false for this template before this PR.

[pwilkin]

Ah, I'm sorry, I was tired and I look at the description and thought it was for something else before looking at the code.

Yes, this is valid, thanks.