Thread safe compiler cache

[CC-Yeh]

Proposed changes

Guard access of cache_.

#2133, #2086

Checklist

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• [x] I have read the CONTRIBUTING document
• [x] I have run pre-commit run --all-files to format my code / installed pre-commit prior to committing changes
• [ ] I have added tests that prove my fix is effective or that my feature works
• [ ] I have updated the necessary documentation (if needed)