Original: should not be used when publishing packages to the public registry.
New     : should not be used when publishing your package to the public registry.

When I read the original phrase, I interpreted it to mean, "Don't publish your package publicly if other packages depend on yours as a local dependency." Although I quickly realized the intended meaning, I believe I would've understood it from the get-go if it were written this new way.

(FWIW, I don't have a strong opinion about this and welcome any feedback.)

References

• Related to docs(package-json): Reword warning about publishing local dependencies #7163 (same issue but on an older branch)
• Ref: https://docs.npmjs.com/cli/v10/configuring-npm/package-json#local-paths