chore(deps): Replace `@babel/polyfill` with `core-js`

[abshierjoel]

Part of #1980

The @babel/polyfill package has been deprecated for some time now, and we should instead rely on core-js directly. I opted to use usage so we wouldn't have to manually find the places to import the polyfills. I have some uncertainty of these changes, so I'd like to see if this passes CI and works in staging as expected. 🤞

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