After looking around and asking, it appears there is no built-in integration of the tkinter and asyncio event loops. That would seem to be a good thing, at least as an example. I wrote a simple hello world which creates an AsyncTk class and uses asyncio-driven event handling. This is clearly incomplete, but might be a useful starting point, even if just as a seed for discussion or as an example for tkinter or asyncio documentation.

Discussion/thread references:

https://mail.python.org/pipermail/python-list/2022-March/905783.html
https://discuss.python.org/t/connecting-asyncio-and-tkinter-event-loops/14722/7

The code in its most basic form is attached. (I have another version which uses pynput to track keyboard and mouse events.)