Fix false-positive error on multiple enum base classes (#12963)

Fixes #12787.

Mypy currently emits a false-positive error for this snippet of code, even though it works fine at runtime (and this exact inheritance structure is used in enum.py in the stdlib):

```
from enum import Enum, Flag
class ReprEnum(Enum): ...
class MyFlag(ReprEnum, Flag): ...
```

This PR fixes that.

mypy/checker.py

@@ -1965,14 +1965,29 @@ def is_final_enum_value(self, sym: SymbolTableNode) -> bool:
         return False
 
     def check_enum_bases(self, defn: ClassDef) -> None:
+        """
+        Non-enum mixins cannot appear after enum bases; this is disallowed at runtime:
+
+            class Foo: ...
+            class Bar(enum.Enum, Foo): ...
+
+        But any number of enum mixins can appear in a class definition
+        (even if multiple enum bases define __new__). So this is fine:
+
+            class Foo(enum.Enum):
+                def __new__(cls, val): ...
+            class Bar(enum.Enum):
+                def __new__(cls, val): ...
+            class Baz(int, Foo, Bar, enum.Flag): ...
+        """
         enum_base: Optional[Instance] = None
         for base in defn.info.bases:
             if enum_base is None and base.type.is_enum:
                 enum_base = base
                 continue
-            elif enum_base is not None:
+            elif enum_base is not None and not base.type.is_enum:
                 self.fail(
-                    f'No base classes are allowed after "{enum_base}"',
+                    f'No non-enum mixin classes are allowed after "{enum_base}"',
                     defn,
                 )
                 break

test-data/unit/check-enum.test

@@ -1903,6 +1903,14 @@ class Third:
 class Mixin:
     pass
 
+class EnumWithCustomNew(enum.Enum):
+    def __new__(cls, val):
+        pass
+
+class SecondEnumWithCustomNew(enum.Enum):
+    def __new__(cls, val):
+        pass
+
 # Correct Enums:
 
 class Correct0(enum.Enum):
@@ -1920,6 +1928,9 @@ class Correct3(Mixin, enum.Enum):
 class RegularClass(Mixin, First, Second):
     pass
 
+class Correct5(enum.Enum):
+    pass
+
 # Correct inheritance:
 
 class _InheritingDataAndMixin(Correct1):
@@ -1934,42 +1945,51 @@ class _CorrectWithDataAndMixin(Mixin, First, Correct0):
 class _CorrectWithMixin(Mixin, Correct2):
     pass
 
+class _CorrectMultipleEnumBases(Correct0, Correct5):
+    pass
+
+class _MultipleEnumBasesAndMixin(int, Correct0, enum.Flag):
+    pass
+
+class _MultipleEnumBasesWithCustomNew(int, EnumWithCustomNew, SecondEnumWithCustomNew):
+    pass
+
 # Wrong Enums:
 
 class TwoDataTypesViaInheritance(Second, Correct2):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Correct2"
     pass
 
-class TwoDataTypesViaInheritanceAndMixin(Second, Correct2, Mixin):  # E: No base classes are allowed after "__main__.Correct2" \
+class TwoDataTypesViaInheritanceAndMixin(Second, Correct2, Mixin):  # E: No non-enum mixin classes are allowed after "__main__.Correct2" \
                                                                     # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Correct2"
     pass
 
-class MixinAfterEnum1(enum.Enum, Mixin):  # E: No base classes are allowed after "enum.Enum"
+class MixinAfterEnum1(enum.Enum, Mixin):  # E: No non-enum mixin classes are allowed after "enum.Enum"
     pass
 
-class MixinAfterEnum2(First, enum.Enum, Mixin):  # E: No base classes are allowed after "enum.Enum"
+class MixinAfterEnum2(First, enum.Enum, Mixin):  # E: No non-enum mixin classes are allowed after "enum.Enum"
     pass
 
 class TwoDataTypes(First, Second, enum.Enum):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 
-class TwoDataTypesAndIntEnumMixin(First, Second, enum.IntEnum, Mixin):  # E: No base classes are allowed after "enum.IntEnum" \
+class TwoDataTypesAndIntEnumMixin(First, Second, enum.IntEnum, Mixin):  # E: No non-enum mixin classes are allowed after "enum.IntEnum" \
                                                                         # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 
 class ThreeDataTypes(First, Second, Third, enum.Enum):  # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second" \
                                                         # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Third"
     pass
 
-class ThreeDataTypesAndMixin(First, Second, Third, enum.Enum, Mixin):  # E: No base classes are allowed after "enum.Enum" \
+class ThreeDataTypesAndMixin(First, Second, Third, enum.Enum, Mixin):  # E: No non-enum mixin classes are allowed after "enum.Enum" \
                                                                        # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second" \
                                                                        # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Third"
     pass
 
-class FromEnumAndOther1(Correct2, Second, enum.Enum):  # E: No base classes are allowed after "__main__.Correct2" \
+class FromEnumAndOther1(Correct2, Second, enum.Enum):  # E: No non-enum mixin classes are allowed after "__main__.Correct2" \
                                                        # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 
-class FromEnumAndOther2(Correct2, Second):  # E: No base classes are allowed after "__main__.Correct2" \
+class FromEnumAndOther2(Correct2, Second):  # E: No non-enum mixin classes are allowed after "__main__.Correct2" \
                                             # E: Only a single data type mixin is allowed for Enum subtypes, found extra "__main__.Second"
     pass
 [builtins fixtures/tuple.pyi]