[Feature Request] Use AnyIO for Python Async

> *In particular, it can interleave I/O and conversion*

If you're implementing an async interface, as a [`trio`](https://trio.readthedocs.io/en/stable/) user, it would be great if you could use [`anyio`](https://github.com/agronholm/anyio) rather than native `asyncio` features. This will enable the code to be used with any async library.

Perhaps the most prominent Python library to support AnyIO is [`fastapi`](https://fastapi.tiangolo.com/async/#write-your-own-async-code), and that's where I'd (eventually) like to make use of `adbc` - asynchronously connecting to databases for displaying data in FastAPI dashboards.

_Originally posted by @dhirschfeld in https://github.com/apache/arrow-adbc/issues/71#issuecomment-1340130033_