The asyncio REPL does not manage the event loop properly

[johnslavik]

Bug report

Bug description:

Most importantly, it doesn't call .close() on it, which blocks GH-140288 and causes surprising warnings on Windows (see GH-141262).

Ideally, we'd employ asyncio.Runner to manage the tricky and ever-changing parts of the lifecycle pipeline correctly.

CC @ZeroIntensity stdlib, topic-repl, topic-asyncio, 3.13, 3.14, 3.15

CPython versions tested on:

CPython main branch, 3.15, 3.14, 3.13

Operating systems tested on:

Linux, Windows, macOS

Linked PRs

• gh-142784: Employ asyncio.Runner in the asyncio REPL #142785