Use `asyncio` synchronization instead of `anyio`

[MarkusSintonen]

Summary

First PR in series of optimizations to improve performance of httpcore and even reach performance levels of aiohttp. Related discussion https://github.com/encode/httpx/issues/3215#issuecomment-2157885121

Previously:

With PR:

Request latency is more stable and the overall duration of the benchmark improves by 3.5x.

The difference diminishes when server latency increases over 100ms or so.

Checklist

• [x] I understand that this PR may be closed in case there was no previous discussion. (This doesn't apply to typos!)
• [x] I've added a test for each change that was introduced, and I tried as much as possible to make a single atomic change.
• [x] I've updated the documentation accordingly.