Expose `@wordpress/element` version used in Site Kit

## Feature Description

This issue is created as a follow-up of #4863 to have another attempt at exposing the version of the `@wordpress/element` package used in Site Kit. It would be nice to expose this package similar to other packages like `api`, `data`, `widgets`, and `modules` so that third-party developers can use it in their plugins.

#4863 attempted to achieve this but unfortunately had to be reverted at the last minute due to missing a few crucial details (read https://github.com/google/site-kit-wp/issues/4863#issuecomment-1303975323).

This issue should use the learnings from #4863 and associated PRs (#6052 & #6105) and take another attempt to implement this.

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## Acceptance criteria

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## Implementation Brief

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### Test Coverage

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## QA Brief

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## Changelog entry

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