[FEATURE] Add support for Github Copilot SDK

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Requirement: A lot of users (including enterprise users) have existing subscription to Github Copilot which gives them access to various AI models including claude. Adding support for Copilot within Claude code would let users use their existing subscriptions within the tool.

Proposed Solution

Integrate the newly launched Copilot SDK to Claude code : copilot-sdk

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

API and model interactions

Use Case Example

_No response_

Additional Context

_No response_