Mixin repr overrides Enum repr in some cases

[rmccampbell7]

BPO	39587
Nosy	@warsaw, @ethanfurman, @miss-islington, @tirkarthi
PRs	bpo-39587: Enum - use correct mixed-in data type #22263 [3.8] bpo-39587: Enum - use correct mixed-in data type (GH-22263) #22265 [3.9] bpo-39587: Enum - use correct mixed-in data type (GH-22263) #22266

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = 'https://github.com/ethanfurman'
closed_at = <Date 2020-09-16.00:01:58.020>
created_at = <Date 2020-02-08.21:01:31.642>
labels = ['3.8', 'type-bug', 'library', '3.9', '3.10']
title = 'Mixin repr overrides Enum repr in some cases'
updated_at = <Date 2020-09-16.00:01:58.020>
user = 'https://bugs.python.org/rmccampbell7'

bugs.python.org fields:

activity = <Date 2020-09-16.00:01:58.020>
actor = 'ethan.furman'
assignee = 'ethan.furman'
closed = True
closed_date = <Date 2020-09-16.00:01:58.020>
closer = 'ethan.furman'
components = ['Library (Lib)']
creation = <Date 2020-02-08.21:01:31.642>
creator = 'rmccampbell7'
dependencies = []
files = []
hgrepos = []
issue_num = 39587
keywords = ['patch']
message_count = 6.0
messages = ['361635', '361667', '376959', '376962', '376963', '376966']
nosy_count = 6.0
nosy_names = ['barry', 'eli.bendersky', 'ethan.furman', 'rmccampbell7', 'miss-islington', 'xtreak']
pr_nums = ['22263', '22265', '22266']
priority = 'normal'
resolution = 'fixed'
stage = 'resolved'
status = 'closed'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue39587'
versions = ['Python 3.8', 'Python 3.9', 'Python 3.10']

[rmccampbell7]

In Python 3.6 the following works:

class HexInt(int):
    def __repr__(self):
        return hex(self)

class MyEnum(HexInt, enum.Enum):
    A = 1
    B = 2
    C = 3

>>> MyEnum.A
<MyEnum.A: 0x1>

However in Python 3.7/8 it instead prints
>>> MyEnum.A
0x1

It uses HexInt's repr instead of Enum's. Looking at the enum.py module it seems that this occurs for mixin classes that don't define __new__ due to a change in the _get_mixins_ method. If I define a __new__ method on the HexInt class then the expected behavior occurs.

[tirkarthi]

Bisecting points to bpo-29577 that introduced this change.