fix(internal): prevent multiple calls to telemetry writer periodic during shutdown

[brettlangdon]

Sometimes periodic will get called while app_shutdown is still running, especially if it is taking longer than expected.

Move locking to adding data to the TelemetryWriter and when calling periodic to prevent multiple calls to periodic at the same time.

Checklist

• Change(s) are motivated and described in the PR description
• Testing strategy is described if automated tests are not included in the PR
• Risks are described (performance impact, potential for breakage, maintainability)
• Change is maintainable (easy to change, telemetry, documentation)
• Library release note guidelines are followed or label changelog/no-changelog is set
• Documentation is included (in-code, generated user docs, public corp docs)
• Backport labels are set (if applicable)
• If this PR changes the public interface, I've notified @DataDog/apm-tees.

Reviewer Checklist

• Title is accurate
• All changes are related to the pull request's stated goal
• Description motivates each change
• Avoids breaking API changes
• Testing strategy adequately addresses listed risks
• Change is maintainable (easy to change, telemetry, documentation)
• Release note makes sense to a user of the library
• 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

[datadog-dd-trace-py-rkomorn]

Datadog Report

Branch report: brettlangdon/fix.telemetry.shutdown
Commit report: d863871
Test service: dd-trace-py

✅ 0 Failed, 492 Passed, 12 Skipped, 2m 15.84s Total Time

[pr-commenter]

Benchmarks

Benchmark execution time: 2024-06-07 18:22:45

Comparing candidate commit dd8bc47 in PR branch brettlangdon/fix.telemetry.shutdown with baseline commit 3bc3051 in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 191 metrics, 9 unstable metrics.