Closes, and does not come back while anything it started is still running.

closeWithGrace is for a caller that is about to exit: it bounds the wait and walks away, because the process is going to take the leftovers with it. A LIBRARY has no such luxury. When run() or close() returns, the caller is entitled to end — and a browser close still in flight holds its transport and its process handle, so the caller ends up hanging on a session it was told it had finished with.

So this gives what it abandoned a second chance to finish before answering. Two bounded waits rather than one unbounded one: a close that is merely SLOW — which on a loaded Windows runner is most of them — lands in the second, and a genuinely deadlocked one still cannot wedge the caller forever. What is still pending after that is returned rather than swallowed, because at that point nothing else is going to release it and the caller deserves to know.

import { closeCompletely } from './close-with-grace.ts';

await closeCompletely({ server: Promise.resolve() }); // [] — nothing was left running
await closeCompletely({ wedged: new Promise(() => {}) }, 10); // ['wedged'] — and it says so