fix: cache Playwright browsers to skip reinstall

[mlqn]

Description

Verification

• Related issues are connected (if applicable)
• Your code builds clean without any errors or warnings
• Manual testing done (required)
• Relevant automated test added (if you find this hard, leave it and we'll help out)

[coderabbitai]

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch fix/playwright-setup

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