feat(integrations): Update integration to new JS interface

[krystofwoldrich]

Updates the React Native integration to use the new factory functions returning plain JS object style.

• needs https://github.com/getsentry/sentry-react-native/pull/3720

[github-actions[bot]]

	Fails
:no_entry_sign:	Please consider adding a changelog entry for the next release.

	Messages
:book:	Do not forget to update Sentry-docs with your feature once the pull request gets approved.

Instructions and example for changelog

Please add an entry to CHANGELOG.md to the "Unreleased" section. Make sure the entry includes this PR's number.

Example:

## Unreleased

- Update integration to new JS interface ([#3721](https://github.com/getsentry/sentry-react-native/pull/3721))

If none of the above apply, you can opt out of this check by adding #skip-changelog to the PR description.

Generated by :no_entry_sign: dangerJS against 67b61f48dd2742aa0acaa91980831e732e828b5a

[github-actions[bot]]

Android (legacy) Performance metrics :rocket:

	Plain	With Sentry	Diff
Startup time	412.23 ms	434.44 ms	22.21 ms
Size	17.73 MiB	19.93 MiB	2.20 MiB

[github-actions[bot]]

Android (new) Performance metrics :rocket:

	Plain	With Sentry	Diff
Startup time	368.04 ms	393.08 ms	25.04 ms
Size	7.15 MiB	8.20 MiB	1.06 MiB

[github-actions[bot]]

iOS (legacy) Performance metrics :rocket:

	Plain	With Sentry	Diff
Startup time	1198.10 ms	1199.45 ms	1.35 ms
Size	2.36 MiB	2.92 MiB	569.46 KiB

[krystofwoldrich]

• closed in favour of backwards compatible changes from https://github.com/getsentry/sentry-react-native/pull/3814