[Do Not merge] Attempting to see if adding a cache will speed up the `sdf::Root` construction

[arjo129]

🦟 Bug fix

Fixes #<NUMBER>

Summary

I'm just checking if adding a cache makes any sense. I probably broke 10 other things along the way and made the entire library thread-unsafe.

Checklist

• [ ] Signed all commits for DCO
• [ ] Added tests
• [ ] Updated documentation (as needed)
• [ ] Updated migration guide (as needed)
• [ ] Consider updating Python bindings (if the library has them)
• [ ] codecheck passed (See contributing)
• [ ] All tests passed (See test coverage)
• [ ] While waiting for a review on your PR, please help review another open pull request to support the maintainers

Note to maintainers: Remember to use Squash-Merge and edit the commit message to match the pull request summary while retaining Signed-off-by messages.

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