refactor: simplify variable naming in HMR client

[chenjiahan]

Summary

• Rename variables for better clarity
• Simplify error clearing and update checking logic

Checklist

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

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[Copilot]

Pull Request Overview

This PR refactors the HMR client code to improve variable naming and simplify error handling logic. The changes focus on making the code more readable and consistent.

• Renamed variables for better clarity (e.g., lastCompilationHash → lastHash, hasCompileErrors → hasBuildErrors)
• Simplified error clearing logic by consolidating state management into clearBuildErrors() function
• Unified message handling by replacing separate errorMessages array with generic messages array

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