Remove support for sx from BranchName component

[llastflowers]

Closes https://github.com/github/primer/issues/5730

Current sx usage: 1

✅ sx usages are only in repos other than github-ui; those usages have been added to the tracking issue

Changelog

Removed

• Remove support for sx from the BranchName component

Rollout strategy

• Major release; if selected, include a written rollout or migration plan

We are using the @primer/styled-react component to mitigate removing sx usage. We will make sure usage is updated upstream before merging.

Merge checklist

• Added/updated tests
• Added/updated documentation
• Added/updated previews (Storybook)
• Changes are SSR compatible
• Tested in Chrome
• Tested in Firefox
• Tested in Safari
• Tested in Edge
• (GitHub staff only) Integration tests pass at github/github (Learn more about how to run integration tests)

[changeset-bot]

🦋 Changeset detected

Latest commit: b5cbf1d

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 2 packages

Name	Type
@primer/react	Major
@primer/styled-react	Major

Not sure what this means? Click here to learn what changesets are.

Click here if you're a maintainer who wants to add another changeset to this PR

[github-actions]

👋 Hi, this pull request contains changes to the source code that github/github depends on. If you are GitHub staff, we recommend testing these changes with github/github using the integration workflow. Thanks!

[github-actions]

size-limit report 📦

Path	Size
packages/react/dist/browser.esm.js	87.94 KB (-0.01% 🔽)
packages/react/dist/browser.umd.js	88.16 KB (+0.07% 🔺)

[primer-integration]

👋 Hi from github/github! Your integration PR is ready: https://github.com/github/github/pull/397512

[Copilot]

Pull Request Overview

This PR removes the deprecated sx prop support from the BranchName component in @primer/react as part of the design system's migration away from styled-components. The component is simplified to use standard CSS modules while maintaining a styled-react wrapper for backward compatibility.

Key changes:

• Remove sx prop support and styled-components dependencies from BranchName
• Simplify component implementation to use direct DOM elements
• Add BranchName to styled-react package exports for migration compatibility

Reviewed Changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
packages/react/src/BranchName/BranchName.tsx	Removes sx prop support, BoxWithFallback usage, and simplifies to direct component rendering
packages/react/src/BranchName/BranchName.docs.json	Removes sx prop from component documentation
packages/styled-react/src/index.ts	Adds BranchName export for backward compatibility
packages/styled-react/src/tests/snapshots/exports.test.ts.snap	Updates snapshot to include BranchName export
.changeset/strange-peas-kiss.md	Documents breaking change and minor styled-react update

[github-actions]

👋 Hi, this pull request contains changes to the source code that github/github depends on. If you are GitHub staff, we recommend testing these changes with github/github using the integration workflow. Thanks!

[francinelucca]

Note: make sure to run integration checks 🙏