fix(ddtrace/tracer): Introduce an optional sync flushing mechanism for serverless use case

[kakkoyun]

Signed-off-by: Kemal Akkoyun kemal.akkoyun@datadoghq.com

WIP

TODO

• Add comprehensive tests
• Make sure this won't break any regular use cases

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-09-25 15:55:10

Comparing candidate commit 0014d9e in PR branch lambda_flush_support with baseline commit 45aa5ed in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 24 metrics, 0 unstable metrics.

[datadog-datadog-prod-us1]

⚠️ Tests

⚠️ Warnings

🧪 1 Test failed

TestMain from github.com/DataDog/dd-trace-go/v2/ddtrace/tracer (Datadog) (✨ Fix with BitsAI)

Failed

PASS
coverage: 69.7% of statements
goleak: Errors on successful test run: found unexpected goroutines:
[Goroutine 19837 in state select, with github.com/DataDog/datadog-go/v5/statsd.(*telemetryClient).run.func1 on top of the stack:
github.com/DataDog/datadog-go/v5/statsd.(*telemetryClient).run.func1()
	C:/Users/runneradmin/go/pkg/mod/github.com/!data!dog/datadog-go/v5@v5.6.0/statsd/telemetry.go:167 +0xc6
created by github.com/DataDog/datadog-go/v5/statsd.(*telemetryClient).run in goroutine 19826
	C:/Users/runneradmin/go/pkg/mod/github.com/!data!dog/datadog-go/v5@v5.6.0/statsd/telemetry.go:163 +0x90
...

ℹ️ Info

❄️ No new flaky tests detected

_{This comment will be updated automatically if new data arrives.
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