chore: migrate automatic vendor sharing e2e from Cypress to Playwright

[ScriptedAlchemy]

Summary

• replace the Cypress-based end-to-end suite in the automatic vendor sharing example with a Playwright implementation
• update Playwright utilities and selectors to match the rendered UI and verify styling for local and remote buttons
• refresh the example README to document Playwright usage and remove legacy Cypress configuration files

Testing

• pnpm --filter automatic-vendor-sharing e2e:ci

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https://chatgpt.com/codex/tasks/task_e_68e4512ec8ac8325892f39c276729487

[ScriptedAlchemy]

@codex resolve merge conflicts, help me rebase pr

[chatgpt-codex-connector]

Summary

• Rebasing the work branch onto base commit 53e568c3c81fc833c2944d84d93cea45eefa9496 completed successfully with no conflicts to resolve.
• Removed stray v8-compile-cache-0 directories so the working tree is clean after the rebase.

Testing

• ⚠️ No tests were run (not requested).

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