Explore using `swift-subprocess` for the test server

Explore using the `swift-subprocess` package to orchestrate the test server instead of going through the Core SDK. This gives us more control and allows us to tie it into structured concurrency primitives.

Locate the test-server orchestration that currently goes through the Core SDK, then review how the swift-subprocess package could replace that path and connect with structured concurrency primitives. The issue names no files or tests; done would require a decided approach and a working test-server orchestration using the selected design.

Written by the indexing model from the issue text.