refactor(samples): modernize syntax in youtube playlist.

[abdulalim110]

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Description

This PR refactors samples/youtube/playlist.js to improve code consistency and readability by adopting modern ES6+ standards.

• Refactored string concatenation to use template literals.

• Implemented object property shorthand for the headers object.

• Ensured consistency with existing modern syntax used in other parts of the same file.

Impact

This is a non-breaking change that improves the quality of the sample code. It provides a better "Developer Experience" (DX) for users who refer to these samples to learn the API.

Testing

• Manual verification of the code structure.

• Ran npm run fix to ensure compliance with Google's style guide (GTS/ESLint).

Additional Information

The changes are isolated to the samples/ directory and do not affect the core library logic or auto-generated API files.

Checklist

• Make sure to open an issue before writing your code!
• Ensure the tests and linter pass
• Code coverage does not decrease
• Appropriate docs were updated
• Appropriate comments were added
• No new warnings or issues will be generated from this change

Fixes #3883 🦕