feat(tracing): add support for DD_TRACE_PROPAGATION_BEHAVIOR_EXTRACT

[MilanGarnier]

Description

Add support for DD_TRACE_PROPAGATION_BEHAVIOR_EXTRACT, which controls how the
tracer handles incoming distributed-trace context during extraction:

• continue (default): preserve the existing behavior and continue the
  extracted trace context.
• restart: create a new root trace with a fresh sampling decision and add a
  span link to the extracted context.
• ignore: discard the incoming context; extract_span returns
  Error::NO_SPAN_TO_EXTRACT, and baggage extraction is disabled.

Changes:

• Add the public PropagationBehaviorExtract enum and parser, with values
  continue, restart, and ignore.
• Add DD_TRACE_PROPAGATION_BEHAVIOR_EXTRACT (default: continue) to tracer
  configuration, config inversion metadata, and telemetry reporting. Both
  programmatic and environment configuration are supported; environment values
  take precedence.
• Apply the behavior in Tracer::extract_span:
  • continue retains the existing extraction path.
  • restart creates a new trace and attaches a span link to the selected
    extracted context. The link records reason=propagation_behavior_extract,
    the selected extraction style in context_headers, the merged sampling
    decision as W3C flags, and the raw W3C tracestate when it belongs to the
    linked context.
  • ignore short-circuits context extraction.
• Store the raw W3C tracestate during extraction so it can be retained on a
  restart link when applicable.
• Update the system-test request handler so restart contexts without a remote
  parent use collision-safe synthetic handles.
• Add unit coverage for configuration precedence/defaults and restart-link
  metadata, sampling flags, and selected-context behavior.
• Simplify Span::add_link(const Span&, ...) to construct the link in one
  step.

This PR is stacked on milan.garnier/span-links-support, which supplies the
underlying span-link support; this diff is scoped to propagation behavior on
extraction.

Motivation

This aligns C++ with the extraction-behavior control available in other
Datadog tracers. It lets services avoid continuing an untrusted or foreign
trace while retaining a correlation link to its context.

System tests: DataDog/system-tests#7279

Jira ticket: APMAPI-1941

[datadog-prod-us1-6]

🎯 Code Coverage (details)
• Patch Coverage: 84.71%
• Overall Coverage: 91.63% (-0.15%)

_{This comment will be updated automatically if new data arrives.
🔗 Commit SHA: 3e874a4 | Docs | Datadog PR Page | Give us feedback!}

[pr-commenter]

Benchmarks

Benchmark execution time: 2026-07-15 10:53:25

Comparing candidate commit 3e874a4 in PR branch milan.garnier/propagation-behavior-extract with baseline commit 58fcb18 in branch milan.garnier/span-links-support.

Found 1 performance improvements and 0 performance regressions! Performance is the same for 7 metrics, 0 unstable metrics.

Explanation

This is an A/B test comparing a candidate commit's performance against that of a baseline commit. Performance changes are noted in the tables below as:

• 🟩 = significantly better candidate vs. baseline
• 🟥 = significantly worse candidate vs. baseline

We compute a confidence interval (CI) over the relative difference of means between metrics from the candidate and baseline commits, considering the baseline as the reference.

If the CI is entirely outside the configured SIGNIFICANT_IMPACT_THRESHOLD (or the deprecated UNCONFIDENCE_THRESHOLD), the change is considered significant.

Feel free to reach out to #apm-benchmarking-platform on Slack if you have any questions.

More details about the CI and significant changes

You can imagine this CI as a range of values that is likely to contain the true difference of means between the candidate and baseline commits.

CIs of the difference of means are often centered around 0%, because often changes are not that big:

---------------------------------(------|---^--------)-------------------------------->
                              -0.6%    0%  0.3%     +1.2%
                                 |          |        |
         lower bound of the CI --'          |        |
sample mean (center of the CI) -------------'        |
         upper bound of the CI ----------------------'

As described above, a change is considered significant if the CI is entirely outside the configured SIGNIFICANT_IMPACT_THRESHOLD (or the deprecated UNCONFIDENCE_THRESHOLD).

For instance, for an execution time metric, this confidence interval indicates a significantly worse performance:

----------------------------------------|---------|---(---------^---------)---------->
                                       0%        1%  1.3%      2.2%      3.1%
                                                  |   |         |         |
       significant impact threshold --------------'   |         |         |
                      lower bound of CI --------------'         |         |
       sample mean (center of the CI) --------------------------'         |
                      upper bound of CI ----------------------------------'

scenario:BM_TraceTinyCCSource

• 🟩 execution_time [-3.200ms; -3.045ms] or [-4.127%; -3.927%]

[MilanGarnier]

@codex review

[chatgpt-codex-connector]

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