Use correct package.json file when publishing new versions

[amgleitman]

Please select one of the following

• I am removing an existing difference between facebook/react-native and microsoft/react-native-macos 👍
• I am cherry-picking a change from Facebook's react-native into microsoft/react-native-macos 👍
• I am making a fix / change for the macOS implementation of react-native
• I am making a change required for Microsoft usage of react-native

Summary

Our ADO pipeline didn't get the news that the package.json file with the right version information now lives in a new spot.

Changelog

[INTERNAL] [FIXED] - Use correct package.json file when publishing new versions

Test Plan

This only affects the publishing pipeline. We'll know when this gets checked in.