Handwriting recognition in Apple Notes

Apple Notes will recognize handwriting, and make it searchable within Apple Notes. However, when I export the note into PDF (e.g., for sharing, for archival), the PDF is no longer searchable.

This is different from Notability or GoodNotes in my experience.

Am I missing something, or is Apple, as usual, making enticing software with annoying and unnecessary limitations? (apologies for the snide remark… I should accept that Apple giveth and Apple taketh away… oops, there I go again!)