Fix llm_request trace context propagation

[will-deines]

Summary

• preserve request-scoped trace context for llm_request instead of falling back to ambient process environment state during final span emission
• normalize propagated trace headers case-insensitively and carry them explicitly through serving and engine request processing
• add regression coverage asserting llm_request stays in the parent distributed trace while receiving its own unique span id

Duplicate-work check

• The only related open PR I found is [Frontend][Tracing] Add support for tracing aborted requests #32162, which adds tracing for aborted requests. It does not address stale trace header reuse, split traces, or llm_request span identity.
• This PR supersedes closed PR Fix llm_request trace context propagation #38672, which was closed because it was based on the wrong fork base. This replacement is based directly on vllm-project/vllm:main.

Testing

• ./.venv/bin/python -m pytest tests/tracing/test_otel.py -v -s (5 passed)
• PRE_COMMIT_HOME=/tmp/pre-commit-vllm-upstream-tracing XDG_CACHE_HOME=/tmp/xdg-cache-vllm-upstream-tracing NPM_CONFIG_CACHE=/tmp/npm-cache-vllm-upstream-tracing ./.venv/bin/pre-commit run --files vllm/tracing/utils.py vllm/tracing/otel.py vllm/tracing/__init__.py vllm/entrypoints/openai/engine/serving.py vllm/entrypoints/pooling/base/serving.py vllm/v1/engine/input_processor.py vllm/v1/engine/output_processor.py tests/tracing/test_otel.py (passed)

AI assistance

AI assistance was used to draft and implement this change. The submitter reviewed the final diff and validated the tests above.

[gemini-code-assist]

Code Review

This pull request enhances OpenTelemetry tracing by improving trace context propagation and header handling. Key changes include making trace header extraction case-insensitive, adding a mechanism to retrieve trace headers from the current OTel context when request headers are missing, and introducing a use_environment_context flag to control fallback behavior to environment variables. Additionally, trace headers are now normalized in the V1 engine input processor, and comprehensive tests have been added to verify these improvements. I have no feedback to provide.