[API] Fix DeepSeek V4.1 /v1/responses empty prompt routing

[hnyls2002]

• Fix /v1/responses returning 400: texts cannot be empty and tokenizer must be initialized for text requests on multimodal DeepSeek V4.1 checkpoints: forward the encoder's prompt_ids, matching Chat Completions.
• Target the dsv4.1 branch from dsv4.1: remaining model and runtime integration #38798; preserve image payloads and encoded image placeholders without requiring --language-model-only or changing PD configuration.
• Add regression coverage using the V4.1 encoder for text-only and image inputs; both cases reproduced empty prompt routing before the fix.
• Related: [Responses] Fix empty-prompt routing for token-first chat encoders (kimi_k3, inkling) #35486 fixes the same routing issue on main for kimi_k3 and inkling. The dsv4.1 branch does not yet contain that helper; when integrating it, dsv41 must also be included in spec_renders_prompt_ids.
• Validation: 45 tests passed across test_serving_responses.py, test_serving_responses_stream.py, and test_encoding_dsv41.py; pre-commit checks passed. Real PD GPU inference has not been run.

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CI States

Latest PR Test (Base): ❌ Run #34557724636
Latest PR Test (Extra): ❌ Run #34557724152
Latest PR Test (AMD ROCm 10): ❌ Run #34557724624

[qqtang-code]

Cross-branch heads-up for whenever dsv4.1 lands on main.

This fix keys the empty-prompt routing on the encoding spec in serving_responses._make_request. main has since refactored that same block (ad7f57c, #35486) into a shared helper:

# serving_chat.py
def _engine_prompt(self, processed_messages, is_multimodal):
    if is_multimodal and not chat_encoding.spec_renders_prompt_ids(self.chat_encoding_spec):
        return "text", processed_messages.prompt
    ...
# chat_encoding.py
def spec_renders_prompt_ids(spec):
    return spec in ("inkling", "kimi_k3")

That whitelist does not contain "dsv41". If the merge keeps main's helper and drops this guard, DeepSeek-V4.1 goes straight back to the bug this PR fixes: the V4.1 encoder is token-first, so processed_messages.prompt is empty and /v1/responses returns

400 texts cannot be empty and tokenizer must be initialized

Adding "dsv41" to spec_renders_prompt_ids (or keeping this guard) resolves it. Verified on 8× RTX 6000D serving deepseek-ai/DeepSeek-V4.1-Flash: with the guard, plain text / instructions / streaming / function tools all return 200; without it, all five input spellings return 400.