[Refactor] Modernize errorHandler with async/await and early returns

[gonzaloriestra]

This PR refactors the errorHandler function in packages/cli-kit/src/public/node/error-handler.ts to use async/await and early returns, replacing a nested if/else and .then() promise chain. This improves readability and maintainability without changing observable behavior.

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PR created automatically by Jules for task 13786756588856414539 started by @gonzaloriestra

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