chore(config): migrate tracer.logStartup

[mtoffl01]

What does this PR do?

Tracer migrates to using Config.logStartup instead of its own config.logStartup.

Motivation

https://datadoghq.atlassian.net/browse/APMAPI-1748

Reviewer's Checklist

• Changed code has unit tests for its functionality at or near 100% coverage.
• System-Tests covering this feature have been added and enabled with the va.b.c-dev version tag.
• There is a benchmark for any new code, or changes to existing code.
• If this interacts with the agent in a new way, a system test has been added.
• New code is free of linting errors. You can check this by running ./scripts/lint.sh locally.
• Add an appropriate team label so this PR gets put in the right place for the release notes.
• Non-trivial go.mod changes, e.g. adding new modules, are reviewed by @DataDog/dd-trace-go-guild.

Unsure? Have a question? Request a review!

[mtoffl01]

"calculated" is an established origin already used by other ddtrace libs such as dotnet, node and java. It essentially represents, "we determined the value of this config based on other factors; we 'calculated' it outselves"

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-12-11 15:56:34

Comparing candidate commit f4f16d7 in PR branch mtoff/logstartup with baseline commit 0f78453 in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 18 metrics, 0 unstable metrics.

[datadog-datadog-prod-us1]

✅ Tests

🎉 All green!

❄️ No new flaky tests detected
🧪 All tests passed

<sub>This comment will be updated automatically if new data arrives.
* Fix with Cursor requires Datadog plugin ≥v2.17.0
🔗 Commit SHA: f4f16d7 | Docs | Datadog PR Page | Was this helpful? Give us feedback!</sub>

[codecov]

Codecov Report

❌ Patch coverage is 21.05263% with 15 lines in your changes missing coverage. Please review.
✅ Project coverage is 54.28%. Comparing base (bee04f0) to head (37fb44d).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
internal/config/config.go	9.09%	10 Missing ⚠️
ddtrace/tracer/option.go	16.66%	5 Missing ⚠️

Additional details and impacted files

Files with missing lines	Coverage Δ
ddtrace/tracer/telemetry.go	87.50% <100.00%> (ø)
ddtrace/tracer/tracer.go	86.40% <100.00%> (+0.19%)	⬆️
ddtrace/tracer/option.go	85.16% <16.66%> (+0.57%)	⬆️
internal/config/config.go	62.82% <9.09%> (-21.67%)	⬇️

... and 80 files with indirect coverage changes

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[mtoffl01]

• chore(config): migrate tracer.logStartup #4214 👈 (View in Graphite)
• main

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