fix: recreate persistent cache directories during save

[hardfist]

Summary

• Recreate persistent cache destination directories before moving staged files so watch-mode saves can write packs after the cache directory is removed.
• Add a JS watch regression that deletes the persistent cache directory between rebuilds and verifies pack files are written again.

Related links

Closes #14723

Checklist

• Tests updated (or not required).
• Documentation updated (or not required).

[codspeed-hq]

Merging this PR will not alter performance

✅ 43 untouched benchmarks
⏩ 47 skipped benchmarks¹

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_{Comparing codex/fix-persistent-cache-watch-delete (407e6db) with main (be555f9)}

Footnotes

1. 47 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩