fix(profiling): support for greenlets [backport 3.10]

[github-actions]

Backport 9fec84d from #14011 to 3.10.

We improve the error handling around greenlet tracking to catch any unexpected errors and prevent the target application from failing to spawn greenlets. One observed case of failure was due to the string table failing to resolve a string (the greenlet name in this case) into a cache key. We expect this kind of errors to be rare, but we add logic to handle them should they occur.

Checklist

• PR author has checked that all the criteria below are met
• The PR description includes an overview of the change
• The PR description articulates the motivation for the change
• The change includes tests OR the PR description describes a testing strategy
• The PR description notes risks associated with the change, if any
• Newly-added code is easy to change
• The change follows the library release note guidelines
• The change includes or references documentation updates if necessary
• Backport labels are set (if applicable)

Reviewer Checklist

• Reviewer has checked that all the criteria below are met
• Title is accurate
• All changes are related to the pull request's stated goal
• Avoids breaking API changes
• Testing strategy adequately addresses listed risks
• Newly-added code is easy to change
• Release note makes sense to a user of the library
• If necessary, 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

[github-actions]

CODEOWNERS have been resolved as:

releasenotes/notes/fix-profiling-greenlet-support-4a873a43e9c4b047.yaml  @DataDog/apm-python
ddtrace/profiling/_gevent.py                                            @DataDog/profiling-python

[github-actions]

Bootstrap import analysis

Comparison of import times between this PR and base.

Summary

The average import time from this PR is: 289 ± 5 ms.

The average import time from base is: 286 ± 5 ms.

The import time difference between this PR and base is: 2.7 ± 0.2 ms.

Import time breakdown

The following import paths have shrunk:

ddtrace.auto 1.238 ms (0.43%)

ddtrace 0.673 ms (0.23%)

ddtrace.internal._unpatched 0.028 ms (0.01%)

json 0.028 ms (0.01%)

json.decoder 0.028 ms (0.01%)

re 0.028 ms (0.01%)

enum 0.028 ms (0.01%)

types 0.028 ms (0.01%)

ddtrace.bootstrap.sitecustomize 0.565 ms (0.20%)

ddtrace.bootstrap.preload 0.565 ms (0.20%)

ddtrace.internal.remoteconfig.client 0.565 ms (0.20%)

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-07-16 16:33:54

Comparing candidate commit f9704bd in PR branch backport-14011-to-3.10 with baseline commit 1f8c272 in branch 3.10.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 487 metrics, 3 unstable metrics.

[github-actions]

This pull request has been automatically closed after a period of inactivity.
After this much time, it will likely be easier to open a new pull request with the
same changes than to update this one from the base branch. Please comment or reopen
if you think this pull request was closed in error.