feat: add Search1API provider with web search DeepSeek models

[fatwang2]

💻 变更类型 | Change Type

• ✨ feat
• 🐛 fix
• ♻️ refactor
• 💄 style
• 👷 build
• ⚡️ perf
• 📝 docs
• 🔨 chore

🔀 变更说明 | Description of Change

Add Search1API provider with web search DeepSeek models support:

• Add Search1API provider configuration
• Integrate DeepSeek R1 series models with web search capability
• Support 4 models:
  • DeepSeek R1 70B
  • DeepSeek R1
  • DeepSeek R1 70B Fast
  • DeepSeek R1 Fast
• Configure model abilities and context window sizes
• Add OpenAI-compatible API integration

📝 补充信息 | Additional Information

All models support real-time web search functionality, making them suitable for tasks requiring up-to-date information. The implementation follows the OpenAI-compatible API pattern for seamless integration.

[vercel]

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[lobehubbot]

👍 @fatwang2

Thank you for raising your pull request and contributing to our Community
Please make sure you have followed our contributing guidelines. We will review it as soon as possible.
If you encounter any problems, please feel free to connect with us.
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[arvinxx]

rebase 下 main

[lobehubbot]

Bot detected the issue body's language is not English, translate it automatically. 👯👭🏻🧑‍🤝‍🧑👫🧑🏿‍🤝‍🧑🏻👩🏾‍🤝‍👨🏿👬🏿

---

rebase under main

[fatwang2]

已增加search: true，已 rebase

[lobehubbot]

Bot detected the issue body's language is not English, translate it automatically. 👯👭🏻🧑‍🤝‍🧑👫🧑🏿‍🤝‍🧑🏻👩🏾‍🤝‍👨🏿👬🏿

---

Search: true, rebase

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.57%. Comparing base (6006175) to head (661d42d).
Report is 3 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6376      +/-   ##
==========================================
+ Coverage   91.42%   97.57%   +6.14%     
==========================================
  Files         728       14     -714     
  Lines       68423     3676   -64747     
  Branches     4609      205    -4404     
==========================================
- Hits        62559     3587   -58972     
+ Misses       5864       89    -5775     

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