Feature Request: Add OpenAI Responses API Compatibility for Codex Desktop

## Feature Request: Add OpenAI Responses API (/v1/responses) Compatibility

### Background

OpenAI has introduced the new **Responses API** (`/v1/responses`) as the evolution of the Chat Completions API, with built-in support for powerful tools (code interpreter, image generation, web search) and structured outputs. OpenAI's **Codex Desktop** natively uses the Responses API as its communication protocol.

DeepSeek API already supports the OpenAI-compatible `/v1/chat/completions` endpoint, but does **not** yet support the `/v1/responses` endpoint. This prevents tools like Codex Desktop from connecting directly to DeepSeek models.

Community solutions like [codex-proxy](https://github.com/icebear0828/codex-proxy) exist to bridge this gap via protocol translation, but they introduce additional latency, complexity, and maintenance overhead.

### Suggestion

Add OpenAI Responses API compatible endpoints to DeepSeek's API service:

```
POST https://api.deepseek.com/v1/responses
POST https://api.deepseek.com/v1/responses/compact
```

Support the standard Responses API request/response format, including:
- `input` field (replacing `messages`)
- Built-in `tools` (e.g., `code_interpreter`, `web_search`)
- `response_format` for structured outputs
- SSE streaming responses

### Why This Matters

1. **Native Codex Desktop Support** — Codex uses Responses API natively. With compatibility, users can point Codex directly to DeepSeek's API endpoint in settings
2. **Eliminate Middleware** — No need for third-party proxy services like codex-proxy, reducing latency and complexity
3. **Keep Pace with Industry Standards** — Responses API is OpenAI's new standard protocol, and more tools will adopt it going forward
4. **Unlock DeepSeek V4 Flash's Potential** — Fast inference + native tool calling is a powerful combination for coding workflows

### Reference

- Codex Proxy project (https://github.com/icebear0828/codex-proxy) implements Chat Completions to Responses API protocol translation, serving as a reference implementation
- OpenAI Responses API docs: https://platform.openai.com/docs/guides/responses-api