Release tooling: Update docs version files when releasing

[JReinhold]

Closes #23000

What I did

• Made the write-changelog script also update https://github.com/storybookjs/storybook/tree/next/docs/versions/next.json or https://github.com/storybookjs/storybook/tree/next/docs/versions/latest.json appropriately
• Added tests for the write-changelog script
• Made the publish workflow sync https://github.com/storybookjs/storybook/tree/next/docs/versions/next.json to main when publishing a prerelease, so it gets part of a new docs site deployment. This is not necessary the other way around, (for patch releases) since we don't need https://github.com/storybookjs/storybook/tree/next/docs/versions/latest.json to be up-to-date on the next branch.

How to test

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

• If this PR should be tested against many or all sandboxes,
  make sure to add the ci:merged or ci:daily GH label to it.
• Make sure this PR contains one of the labels below.

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

[shilman]

I assume that you ensure that this never gets called in any other scenarios? Future release? Canary release?

[JReinhold]

That's a good point. For now we only support the two release types, so it's hard to come up with how the logic would be if there were other types of releases here.