gh-140947: fix contextvars handling for server tasks in asyncio

[kumaraditya303]

• Issue: context variables can leak out of asyncio.Task #140947

[Kludex]

Any chance this can be considered a security issue?

[kumaraditya303]

Any chance this can be considered a security issue?

There are a lot of moving parts in fixing this and this PR only fixes the non-ssl part, ssl remains remains to be fixed.
IMO it is too risky to backport to security branches, I am in favor of backport to bug-fixes branches after a careful review.