feat: support disablement of APM Tracing (the product)

[dmehala]

Description

Supersede #217

Motivation

1. Simplify the Implementation
   While the original approach worked, I identified a more straightforward way to reach the same goals with fewer moving parts and a clearer mental model.
2. Clarify Underspecified Behavior
   Some behaviors, especially around context extraction, aren’t fully defined in the RFC yet. Rather than making assumptions, we took the opportunity to clarify and solidify these behaviors.
3. Improve Long-Term Maintainability
   Reusing existing constructs and patterns makes the codebase easier to understand, test, and evolve. This rework brings the implementation closer to that goal.

Improvements (non-exhaustive)

• Avoided injecting empty tracing context, which required adding support to delete headers on the integration side.
• Added more comprehensive tests to cover edge cases.
• Aligned API design for trace source attribution, moved from injection options to span-level attributes for clearer semantics.
• Simplified sampling logic by using existing rule-based mechanisms rather than introducing new types or abstractions.
• Clarified the API for controlling stats computation, improving long term maintainability.
• Validated extracted trace source to ensure consistency and reduce potential for errors.
• Reused existing concepts and components, avoiding the need for new structures and reducing the risk of regressions.

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-07-17 15:37:08

Comparing candidate commit 3ae4854 in PR branch dmehala/disable-tracing with baseline commit 31f263f in branch main.

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

scenario:BM_TraceTinyCCSource

• 🟥 execution_time [+3.940ms; +4.051ms] or [+5.418%; +5.571%]

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 90.82569% with 10 lines in your changes missing coverage. Please review.

Project coverage is 86.51%. Comparing base (31f263f) to head (3ae4854).

Files with missing lines	Patch %	Lines
include/datadog/trace_source.h	46.15%	7 Missing ⚠️
src/datadog/telemetry/telemetry_impl.cpp	0.00%	2 Missing ⚠️
include/datadog/dict_writer.h	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #224      +/-   ##
==========================================
+ Coverage   86.45%   86.51%   +0.05%     
==========================================
  Files          80       82       +2     
  Lines        5251     5347      +96     
==========================================
+ Hits         4540     4626      +86     
- Misses        711      721      +10     

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