docs: remove HomeBackground and navTransparent hack

[SoonIter]

Summary

docs: remove HomeBackground and navTransparent hack

Related links

rstackjs/rstack-doc-ui#55

Checklist

• Tests updated (or not required).
• Documentation updated (or not required).

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[Copilot]

Pull Request Overview

This PR removes a workaround for transparent navigation on the home page by eliminating the HomeBackground component hack and upgrading the @rstack-dev/doc-ui package to version 1.12.0, which likely handles this functionality natively.

• Removed the deprecated HomeBackground component import and usage with inline style override
• Updated @rstack-dev/doc-ui from 1.11.0 to 1.12.0
• Updated transitive dependencies (framer-motion and motion-dom) to align with the new doc-ui version

Reviewed Changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated no comments.

File	Description
website/theme/pages/index.tsx	Removed HomeBackground import and its usage with the transparent navigation hack
website/package.json	Upgraded @rstack-dev/doc-ui to version 1.12.0
pnpm-lock.yaml	Updated lockfile entries for @rstack-dev/doc-ui and its transitive dependencies (framer-motion, motion-dom)

Files not reviewed (1)

• pnpm-lock.yaml: Language not supported

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[github-actions]

📦 Binary Size-limit

Comparing d1a5833 to chore(deps): update dependency glob to v11.1.0 [security] (#12223) by renovate[bot]

🙈 Size remains the same at 47.46MB

[chenjiahan]

👍

[codspeed-hq]

CodSpeed Performance Report

Merging #12224 will not alter performance

_{Comparing syt/upgrade-rstack-doc-ui (d1a5833) with main (061307b)}

Summary

✅ 17 untouched