Add support for Chrome Writer API

Problem/Motivation

Currently we only use the prompt library to perform generic AI calls. This is still experimental and does not
take advantage of browser specific APIs optimized for certain tasks.

Chrome provides a Writer API which allows applications to generate and improve text using the on-device AI model.

Reference: https://developer.chrome.com/docs/ai/writer-api

We should implement support for it.

Proposed resolution

1. Add a writer operation type.
2. Ensure the frontend loads the Writer API when supported by the browser.
3. Add provider support to send prompts and receive generated text.

Remaining tasks

• Implement writer operation.
• Add frontend detection for Writer API.
• Integrate writer response handling.

User interface changes

None.