Currently, enum.auto doesn't work with the new (Py3.10) StrEnum: `class E(enum.StrEnum): a = enum.auto()` results in `TypeError: 1 is not a string`.

I would guess that the most reasonable behavior for auto() in a StrEnum would be to return the name itself, as implemented in the AutoName example at https://docs.python.org/3.10/library/enum.html#using-automatic-values.  I believe that this may just be a matter of copying the corresponding `_generate_next_value_` implementation into the definition of StrEnum?

A good idea.

Since the Python opinion of enum members is that they be upper-cased, and every magic string constant I have seen is lower-case, `StrEnum._generate_next_value_` should lower case the name.  Users can substitute their own `_gnv_` for different behavior.