[Feature]: Free OpenAI-Compatible Demo Endpoint with Built-In Monetization via ChatADy

### Issue Checklist

- [x] I understand that issues are for reporting problems and requesting features, not for off-topic comments, and I will provide as much detail as possible to help resolve the issue.
- [x] I have checked the pinned issues and searched through the existing [open issues](https://github.com/CherryHQ/cherry-studio/issues), [closed issues](https://github.com/CherryHQ/cherry-studio/issues?q=is%3Aissue%20state%3Aclosed), and [discussions](https://github.com/CherryHQ/cherry-studio/discussions) and did not find a similar suggestion.
- [x] I have provided a short and descriptive title so that developers can quickly understand the issue when browsing the issue list, rather than vague titles like "A suggestion" or "Stuck."
- [x] The latest version of Cherry Studio does not include the feature I am suggesting.

### Platform

macOS

### Version

v2.0.9

### Is your feature request related to an existing issue?

No

### Desired Solution

Hi! We’d like to offer this project a free OpenAI-compatible API endpoint that can be used as free optional hosted inference backend.

The endpoint follows the familiar OpenAI API format, so integration should be minimal. The main difference is that responses include a small sponsored message, which helps us cover the inference costs and keep the endpoint free.

**Example:**

```
[normal model response]

Sponsored: Advertise here via ChatADy.com
```

**Why this could be useful?**

- Free inference for users trying out the project
- OpenAI-compatible API, so existing clients require little or no modification
- No infrastructure or model hosting costs for the project maintainers
- Can be offered as an optional demo/default provider without replacing existing integrations
- Gives new users a lower-friction way to get the project running

We’re also happy to implement the integration ourselves and submit a PR, including configuration, documentation, and any UI/provider changes required.

If this sounds useful, we can put together the implementation so maintainers only need to review it.

### Alternative Solutions

None

### Additional Information

No additional information

No files, tests, or entry points are named. Start by reviewing the existing provider configuration, API integration, and UI patterns to determine where an optional OpenAI-compatible endpoint belongs. Done should include the endpoint configuration, sponsored-response handling, any required provider or UI changes, and documentation.

Written by the indexing model from the issue text.