Enum `_ignore_`'d names and private names are treated like normal members

Bug Report

To Reproduce

from enum import Enum
from typing import TYPE_CHECKING


class Foo(Enum):
    __str__ = lambda self: "blah"
    _ignore_ = ["ignored"]
    ignored = lambda _: "blah"
    _Foo__private = lambda _: "blah"


print(Foo.__members__)  # {}

print(Foo.__str__)  # <function Foo.<lambda> at 0x...>
if TYPE_CHECKING:
    reveal_type(Foo.__str__)  # note: Revealed type is "def () -> builtins.str" ✅

print(hasattr(Foo, "_ignore_"))  # False
if TYPE_CHECKING:
    reveal_type(Foo._ignore_)  # error: "type[Foo]" has no attribute "_ignore_"  [attr-defined] ✅

print(hasattr(Foo, "ignored"))  # False
if TYPE_CHECKING:
    reveal_type(Foo.ignored)  # note: Revealed type is "Literal[__main__.Foo.ignored]?" ❌

print(Foo._Foo__private)  # <function Foo.<lambda> at 0x...>
if TYPE_CHECKING:
    reveal_type(Foo._Foo__private)  # note: Revealed type is "Literal[__main__.Foo._Foo__private]?" ❌

https://mypy-play.net/?mypy=latest&python=3.13&gist=ea296898a9c0e29c550b6154fb2cb594

Actual Behavior

main.py:16: note: Revealed type is "def () -> builtins.str"
main.py:20: error: "type[Foo]" has no attribute "_ignore_"  [attr-defined]
main.py:20: note: Revealed type is "Any"
main.py:24: note: Revealed type is "Literal[__main__.Foo.ignored]?"
main.py:28: note: Revealed type is "Literal[__main__.Foo._Foo__private]?"
Found 1 error in 1 file (checked 1 source file)

Your Environment

• Mypy version used: 1.14.1
• Python version used: 3.13

Reproduce the example with mypy 1.14.1 on Python 3.13, focusing on Enum handling of str, ignore, ignored, and the name-mangled private member. Trace the type-checking path that classifies Enum attributes and add regression coverage so ignored and private names are not treated as normal members.