[Task] Send copilot-sdk as the default SDK integration ID

## Outcome

The Copilot SDK launches its bundled runtime with `Copilot-Integration-Id: copilot-sdk` for default SDK traffic while preserving explicit registered integration overrides.

## Current problem

The SDK currently inherits the direct CLI default and sends `copilot-developer-cli` unless the host sets `GITHUB_COPILOT_INTEGRATION_ID`. CAPI therefore classifies default SDK traffic as direct CLI traffic. `Copilot-Harness-Id: copilot-sdk` does not solve this because the SDK and standalone CLI share that harness value.

## SDK team ownership

The Copilot SDK team owns the launch-path behavior in this issue. Assign an SDK engineering DRI before implementation and link the implementation pull requests for every affected language or shared launcher.

## Scope

- Set `GITHUB_COPILOT_INTEGRATION_ID=copilot-sdk` when the SDK launches the bundled CLI or runtime and the host did not provide an explicit integration override
- Preserve host-provided registered integration IDs exactly
- Apply the behavior consistently across supported SDK language surfaces or in the shared launch layer used by them
- Keep standalone Copilot CLI defaulting to `copilot-developer-cli`
- Keep `Copilot-Harness-Id` as supporting telemetry only
- Coordinate rollout and compatibility normalization with github/copilot-api#37988

## Acceptance criteria

- [ ] Default SDK requests send `Copilot-Integration-Id: copilot-sdk`
- [ ] A host-provided registered integration override remains effective
- [ ] Standalone CLI requests continue to send `copilot-developer-cli`
- [ ] Tests cover default behavior and explicit overrides across supported SDK launch paths
- [ ] An SDK engineering DRI and implementation pull request are linked here
- [ ] CAPI telemetry confirms default SDK traffic transitions from `copilot-developer-cli` to `copilot-sdk`

## Dependencies and references

- Parent epic github/copilot#30409
- SDK App-token plumbing github/copilot#30423
- CAPI integration allowlist and migration github/copilot-api#37988
- ADR github/copilot#30449

首先定位捆绑的 CLI/runtime 启动路径以及集成标头相关测试，然后比较各受支持 SDK 表面的默认值处理和主机提供的覆盖处理。完成的标准是：默认 SDK 流量使用 SDK 集成 ID，显式覆盖保持不变，独立 CLI 的行为得到保留，并且必要的测试、DRI、实现链接和 telemetry 确认均已具备。

由索引模型根据 Issue 内容生成。