I have updated the PersistentTaskGroup implementation referring asyncio.TaskGroup and added more detailed test cases, which works with the latest Python 3.11 GitHub checkout.

https://github.com/achimnol/aiotools/pull/36/files

Please have a look at the class docstring.
There are two different usage: async context manager vs. attributes of long-lived objects.

One of the point is to "revive" asyncio.gather() with return_exceptions=True but let it handle/report exceptions immediately with customizable exception handler.

Currently two-phase shutdown is not implemented yet as I'm still thinking about how to adapt the current implementation.