Look into creating a shared subprocess implementation between backends

[agronholm]

Things to check first

• I have searched the existing issues and didn't find my feature already requested there

Feature description

We should take a stab at creating a more low-level subprocess implementation that only relies on a minimum set of functionality from each backend, just like the threading API.

Use case

Currently the asyncio subprocess API is a bit iffy from AnyIO's perspective. There are a lot of moving parts which we don't control, and cases where we use undocumented methods (StreamReader.set_exception() as an example). A new implementation, if possible, might make it easier to further develop the AnyIO subprocess APIs.

[gschaffner]

Another point in favor of this is that avoiding asyncio's subprocess API would be the easiest way to resolve the various asyncio-specific issues mentioned in #828.