Event loop integration

This issue is mostly for me to understand how we can move forward with [the switch to AnyIO](https://github.com/ipython/ipykernel/pull/1079) with regards to event loop integration.
It looks like this is currently done manually by the host event loop, which must call `kernel.do_one_iteration()` [regularly](https://ipython.readthedocs.io/en/stable/config/eventloops.html#integrating-with-a-new-event-loop-in-the-kernel).
I am wondering if we could use something like [Trio's guest mode](https://trio.readthedocs.io/en/stable/reference-lowlevel.html#using-guest-mode-to-run-trio-on-top-of-other-event-loops) instead. There would be no need to worry about low-level details and manually run ipykernel's event loop.

cc @Carreau