Private members (__underscored) in an Enum are incorrectly considered members of the enum

Bug Report

Mypy, at least versions 1.17.1 and the latest 1.19.1 incorrectly classifies private members as Enum members and tags them as final.

But, since Python 3.11, private members are not enum members, see https://docs.python.org/3/howto/enum.html#private-names

To Reproduce

https://mypy-play.net/?gist=afd9e4e68abe69277d97eb42f33adbcf

from typing import ClassVar
from enum import IntEnum

class WithDocReference:
  __doc_reference: ClassVar[str]

class MyEnum(WithDocReference, IntEnum):
  __doc_reference = "https://www.google.com"
  A = 1
  B = 2

Expected Behavior

Type checks without error.

Actual Behavior

mypy 1.17.1 fails with

$ mypy test.py
test.py:8: error: Cannot override writable attribute "__doc_reference" with a final one  [misc]
Found 1 error in 1 file (checked 1 source file)

mypy 1.19.1 has an additional error.

Your Environment

• Mypy version used: 1.17.1 and 1.19.1
• Mypy command-line flags: None
• Mypy configuration options from mypy.ini (and other config files): None
• Python version used: 3.11.9

Edited: private names should start with two underscores and not one

Reproduce the issue from the linked mypy-play gist or the test.py example with Python 3.11 and the reported mypy versions. Compare the result with Python's documented handling of private Enum names; the work is done when the example type-checks without the reported errors and the behavior is covered by a regression test.