fix: add HTTP status code check in BraveSearchProvider

[wangyanfu2]

• Add status code validation after reading response body, consistent with TavilySearchProvider and PerplexitySearchProvider

📝 Description

🗣️ Type of Change

• 🐞 Bug fix (non-breaking change which fixes an issue)
• ✨ New feature (non-breaking change which adds functionality)
• 📖 Documentation update
• ⚡ Code refactoring (no functional changes, no api changes)

🤖 AI Code Generation

• 🤖 Fully AI-generated (100% AI, 0% Human)
• 🛠️ Mostly AI-generated (AI draft, Human verified/modified)
• 👨‍💻 Mostly Human-written (Human lead, AI assisted or none)

🔗 Related Issue

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☑️ Checklist

• My code/docs follow the style of this project.
• I have performed a self-review of my own changes.
• I have updated the documentation accordingly.

[afjcjsbx]

@wangyanfu2 thanks for your PR!

[Orgmar]

@wangyanfu2 BraveSearchProvider之前缺少HTTP状态码校验确实容易踩坑，和Tavily、Perplexity那边对齐之后整体一致性好多了，这种细节修复很有价值。

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