We would like to present for feedback a new version of PEP 654, which incorporates the feedback we received in the discussions so far:
https://www.python.org/dev/peps/pep-0654/
The reference implementation has also been updated along with the PEP.

The changes we made since the first post are:

1. Instead of ExceptionGroup(BaseException), we will have two new builtin types: BaseExceptionGroup(BaseException) and ExceptionGroup(BaseExceptionGroup, Exception).
This is so that "except Exception" catches ExceptionGroups (but not BaseExceptionGroups). BaseExceptionGroup.__new__ inspects the wrapped exceptions, and if they are all Exception subclasses, it creates an ExceptionGroup instead of a BaseExceptionGroup.  

2. The exception group classes are not final - they can be subclassed and split()/subgroup() work correctly if the subclass overrides the derive() instance method as described here: https://www.python.org/dev/peps/pep-0654/#subclassing-exception-groups

3. We had some good suggestions on formatting exception groups, which we have implemented as you can see in the output shown for the examples in the PEP.

4. We expanded the section on handling Exception Groups, to show how subgroup can be used (with side effects) to do something for each leaf exception, and how to iterate correctly when the tracebacks of leaf exceptions are needed: https://www.python.org/dev/peps/pep-0654/#handling-exception-groups

5. We expanded the sections on rationale and backwards compatibility to explain our premise and expectations regarding how exception groups will be used and how the transition to using them will be managed.

6. We added several items to the rejected ideas section.

We did not receive any comments (or make any changes) to the proposed semantics of except*, hopefully this is because everyone thought they are sensible.

Irit, Yury and Guido