feat(llmobs): [MLOB-2681] instrument openai responses with llm

[XG-xin]

This PR add LLM tracing/instrumentation for the OpenAI Responses endpoint.

For stream response, we will only get the response.completed chunk because it includes all metadata. Since there's only one response object that is present in each stream chunk, we append it as the first item in streamed_chunks.

This PR only handles function tool, and we might want to support other type of tools (i.e file search) in the furture.

Checklist

• PR author has checked that all the criteria below are met
• The PR description includes an overview of the change
• The PR description articulates the motivation for the change
• The change includes tests OR the PR description describes a testing strategy
• The PR description notes risks associated with the change, if any
• Newly-added code is easy to change
• The change follows the library release note guidelines
• The change includes or references documentation updates if necessary
• Backport labels are set (if applicable)

Reviewer Checklist

• Reviewer has checked that all the criteria below are met
• Title is accurate
• All changes are related to the pull request's stated goal
• Avoids breaking API changes
• Testing strategy adequately addresses listed risks
• Newly-added code is easy to change
• Release note makes sense to a user of the library
• If necessary, author has acknowledged and discussed the performance implications of this PR as reported in the benchmarks PR comment
• Backport labels are set in a manner that is consistent with the release branch maintenance policy

[github-actions]

CODEOWNERS have been resolved as:

.riot/requirements/1458d7e.txt                                          @DataDog/apm-python
.riot/requirements/164ce6e.txt                                          @DataDog/apm-python
.riot/requirements/1a18a5a.txt                                          @DataDog/apm-python
.riot/requirements/1dd6795.txt                                          @DataDog/apm-python
.riot/requirements/41b0f95.txt                                          @DataDog/apm-python
.riot/requirements/77994b3.txt                                          @DataDog/apm-python
.riot/requirements/c050b53.txt                                          @DataDog/apm-python
.riot/requirements/e3b63a1.txt                                          @DataDog/apm-python
releasenotes/notes/openai-responses-llm-2194499974f7324e.yaml           @DataDog/apm-python
tests/contrib/openai/cassettes/v1/response_error.yaml                   @DataDog/ml-observability
tests/contrib/openai/cassettes/v1/response_function_call.yaml           @DataDog/ml-observability
tests/contrib/openai/cassettes/v1/response_function_call_streamed.yaml  @DataDog/ml-observability
ddtrace/contrib/integration_registry/registry.yaml                      @DataDog/apm-core-python @DataDog/apm-idm-python
ddtrace/contrib/internal/openai/_endpoint_hooks.py                      @DataDog/ml-observability
ddtrace/contrib/internal/openai/utils.py                                @DataDog/ml-observability
ddtrace/llmobs/_integrations/openai.py                                  @DataDog/ml-observability
ddtrace/llmobs/_integrations/utils.py                                   @DataDog/ml-observability
riotfile.py                                                             @DataDog/apm-python
supported_versions_output.json                                          @DataDog/apm-core-python
supported_versions_table.csv                                            @DataDog/apm-core-python
tests/contrib/openai/test_openai_llmobs.py                              @DataDog/ml-observability
tests/contrib/openai/utils.py                                           @DataDog/ml-observability
tests/snapshots/tests.contrib.openai.test_openai.test_response_error.json  @DataDog/apm-python
tests/snapshots/tests.contrib.openai.test_openai.test_response_stream.json  @DataDog/apm-python
tests/snapshots/tests.contrib.openai.test_openai.test_response_tools_stream.json  @DataDog/apm-python
.riot/requirements/109d638.txt                                          @DataDog/apm-python
.riot/requirements/13c42e3.txt                                          @DataDog/apm-python
.riot/requirements/1ce4e3f.txt                                          @DataDog/apm-python
.riot/requirements/1e8124b.txt                                          @DataDog/apm-python
.riot/requirements/35f0cba.txt                                          @DataDog/apm-python
.riot/requirements/5301b11.txt                                          @DataDog/apm-python

[github-actions]

Bootstrap import analysis

Comparison of import times between this PR and base.

Summary

The average import time from this PR is: 274 ± 2 ms.

The average import time from base is: 276 ± 2 ms.

The import time difference between this PR and base is: -2.2 ± 0.1 ms.

Import time breakdown

The following import paths have shrunk:

ddtrace.auto 2.067 ms (0.76%)

ddtrace.bootstrap.sitecustomize 1.398 ms (0.51%)

ddtrace.bootstrap.preload 1.398 ms (0.51%)

ddtrace.internal.remoteconfig.client 0.664 ms (0.24%)

ddtrace 0.669 ms (0.24%)

ddtrace.internal._unpatched 0.030 ms (0.01%)

json 0.030 ms (0.01%)

json.decoder 0.030 ms (0.01%)

re 0.030 ms (0.01%)

enum 0.030 ms (0.01%)

types 0.030 ms (0.01%)

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-06-17 01:58:38

Comparing candidate commit 37aa590 in PR branch xinyuan/openai-responses-llm with baseline commit d30bcd7 in branch main.

Found 0 performance improvements and 2 performance regressions! Performance is the same for 563 metrics, 7 unstable metrics.

scenario:iastaspects-replace_aspect

• 🟥 execution_time [+428.760ns; +550.212ns] or [+9.095%; +11.671%]

scenario:telemetryaddmetric-1-distribution-metric-1-times

• 🟥 execution_time [+226.052ns; +314.762ns] or [+7.721%; +10.751%]

[Yun-Kim]

Minor nits but good to merge once addressed!