Modernization of asyncio infrastructure / Deprecate Tornado

[fjetter]

This is an issue to track efforts towards some modernization efforts of our asyncio infrastructure.

Very roughly this is about

• Addressing all warnings triggered by py3.10
• Slowly migrating away from tornado
• Deal with anti-patterns around our usage of futures, tasks and callbacks, e.g. for better exception handling

Related issues

• [x] https://github.com/dask/distributed/issues/6048
• [x] https://github.com/dask/distributed/issues/6050
• [x] https://github.com/dask/distributed/issues/6049
• [x] https://github.com/dask/distributed/issues/6051

[Zac-HD]

I'd strongly recommend migrating to anyio, which can be done incrementally. Here's a page listing some of the productivity and correctness benefits!

Once you're fully migrated, it would also be easy to add Trio support - at that point, it's purely a "turn on the tests" exercise. See also discussion in https://github.com/dask/distributed/issues/6201.