Docs: Writing addons changes for peer-deps

[jonniebigodes]

What I did

With this small pull request, the writing addons page was updated to factor in upcoming changes on peer-dependency handling with Storybook.

What was done:

• Polished the documentation including:
  • Removing the peer dependency section
  • Updating the package.json example to match the expected behavior provided in the Addon kit.
  • Minor tweaks

@JReinhold when you have a moment in your busy schedule, can you take a look at it and let me know of any feedback you may have? Thanks in advance.

Checklist for Contributors

Testing

The changes in this PR are covered in the following automated tests:

• stories
• unit tests
• integration tests
• end-to-end tests

Manual testing

This section is mandatory for all contributions. If you believe no manual test is necessary, please state so explicitly. Thanks!

Documentation

• Add or update documentation reflecting your changes
• If you are deprecating/removing a feature, make sure to update
  MIGRATION.MD

Checklist for 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:

  Available labels

  • bug: Internal changes that fixes incorrect behavior.
  • maintenance: User-facing maintenance tasks.
  • dependencies: Upgrading (sometimes downgrading) dependencies.
  • build: Internal-facing build tooling & test updates. Will not show up in release changelog.
  • cleanup: Minor cleanup style change. Will not show up in release changelog.
  • documentation: Documentation only changes. Will not show up in release changelog.
  • feature request: Introducing a new feature.
  • BREAKING CHANGE: Changes that break compatibility in some way with current major version.
  • other: Changes that don't fit in the above categories.

🦋 Canary release

This PR does not have a canary release associated. You can request a canary release of this pull request by mentioning the @storybookjs/core team here.

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

[JReinhold]

Great job! 🫶

[jonniebigodes]

@JReinhold thank you so much for taking the time to review this. Appreciate it 🙏 . Going to merge this once the checklist clears.