Maintenance: Remove need for react as peerDependency

[ndelangen]

Reverts #23882

What I did

I found out the problem that was causing #23876, so instead of reverting the whole thing, we fix it proper.

How to test

To reproduce:

1. clone the react-parallax-tilt repo
2. checkout the v1.7.161 tag, which is where the issue was found: https://github.com/mkosir/react-parallax-tilt/tree/v1.7.161
3. run npm run start-storybook - it should work
4. remove @storybook/addon-essentials and @storybook/manager-api
5. run npm install then npm run start-storybook - it should fail
6. still with those dependencies removed, change the storybook dependencies to the canary of this PR: 0.0.0-pr-23897-sha-78c2d886
7. run npm run start-storybook - it should work!

Checklist

• Make sure your changes are tested (stories and/or unit, integration, or end-to-end tests)
• Make sure to add/update documentation regarding your changes
• If you are deprecating/removing a feature, make sure to update
  MIGRATION.MD

Maintainers

• When this PR is ready for testing, make sure to add ci:normal, ci:merged or ci:daily GH label to it to run a specific set of sandboxes. The particular set of sandboxes can be found in code/lib/cli/src/sandbox-templates.ts
• Make sure this PR contains one of the labels below.

["cleanup", "BREAKING CHANGE", "feature request", "bug", "build", "documentation", "maintenance", "dependencies", "other"]

🦋 Canary release

This pull request has been released as version 0.0.0-pr-23897-sha-78c2d886. Install it by pinning all your Storybook dependencies to that version.

More information

Published version	0.0.0-pr-23897-sha-78c2d886
Triggered by	@yannbf
Repository	storybookjs/storybook
Branch	revert-23882-revert-23496-norbert/react-peerdep-webpack-builder-removal
Commit	78c2d886
Datetime	Mon Aug 21 07:26:27 UTC 2023 (1692602787)
Workflow run	5923278529

To request a new release of this pull request, mention the @storybookjs/core team.

core team members can create a new canary release here or locally with gh workflow run --repo storybookjs/storybook canary-release-pr.yml --field pr=23897

[yannbf]

[vanessayuenn]

Hey @ndelangen can you please fill out "how to test" and specifically include the steps to ensure the previous breakage doesn't happen again?