Replace flaky GIL/performance test with a deterministic heartbeat-based GIL probe

[xupinjie]

Description

Replace flaky GIL/performance test with a deterministic heartbeat-based GIL probe

Type of Change

Please select (at least one):

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation / examples / tutorials / demos
• Supporting functionality change (fix or feature in documentation generation, helper scripts, ...)
• Refactoring / internal change
• Other (please describe):

Testing

Checklist for testing:

• Tests added or updated if/as needed
• Repository test runner executed: scripts/run_tests.sh

Optionally, add a brief description.

Documentation, Examples, Tutorials, Demos

Checklist for documentation:

• User-facing documentation updated if/as needed (including API docs)
• Examples / tutorials / demos updated or added (if relevant)
• Limitations and constraints documented (if relevant)
• Performance documented (if relevant)
• Documentation building successful & checks outlined in the Documentation Checks section of the Contribution Guide are performed

Optionally, add a brief description.

Code Quality

Checklist for dependencies:

• Dependencies updated in the relevant pyproject.toml if/as needed
• Code formatted according to the Code Formatting Guide

Optionally, add a brief description.

Related Issues / Context

If applicable, link related issues, discussions etc.

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DCO / Sign-Off

Please refer to the section on Signing Your Work & Developer Certificate of Origin (DCO)
in the Contribution Guide before submitting your contribution.

References

For additional details, please refer to the Contribution Guide.
The following guides are available (referenced in the Contribution Guide for further details):

• docs/guides/CONTRIBUTION_GUIDE.md
• docs/guides/DEVELOPMENT_GUIDE.md
• docs/guides/DOCUMENTATION_SETUP_GUIDE.md
• docs/guides/FORMATTING_GUIDE.md

Please also refer to the summary checklist in the Contribution Guide,
which is a guideline for what to consider when submitting your contribution and covers the same topics as the checklists above.

[xupinjie]

/build

[RmSchaffert]

Thank you!

[RmSchaffert]

Please add a sign-off for the commit.

Sing-off needed for the commit

[RmSchaffert]

Thanks!