Bad error with Protocol and class heirarchy with overloads

I'm trying to implement a protocol that mimics QFileSystemModel so that I can use that protocol to define a new custom class. The protocol definition is generating a mypy error ( error: Definition of "index" in base class "QAbstractItemModel" is incompatible with definition in base class "FileSystemModelProtocol")
I've checked with pyright and pytype and neither report an error.

To Reproduce

import typing
from PyQt6 import QtCore, QtGui


class FileSystemModelProtocol(typing.Protocol):
    """Define the subset of QFileSystemModel methods used...for defining a class with the same behavior"""
    @typing.overload
    def index(self, row: int, column: int, parent: QtCore.QModelIndex = ...) -> QtCore.QModelIndex: ...
    @typing.overload
    def index(self, row: typing.Optional[str], column: int = ...) -> QtCore.QModelIndex: ...
    def index(self, row: typing.Optional[int | str] = ..., column: int = ..., parent: QtCore.QModelIndex = ...) -> QtCore.QModelIndex: ...


class CustomFileSystemModel(QtGui.QFileSystemModel, FileSystemModelProtocol):  # error: Definition of "index" in base class "QAbstractItemModel" is incompatible with definition in base class "FileSystemModelProtocol"
    pass


class TableModel(QtCore.QAbstractTableModel, FileSystemModelProtocol):
    def index_from_str(self, path: str) -> QtCore.QModelIndex:
        return QtCore.QModelIndex()  # TODO: lookup with path

    def index(self, row: typing.Optional[int | str] = None, column: int = 0, parent: QtCore.QModelIndex = QtCore.QModelIndex()) -> QtCore.QModelIndex:
        if isinstance(row, str):
            return self.index_from_str(row)
        if isinstance(row, int):
            return super().index(row, column, parent)
        return QtCore.QModelIndex()


c = CustomFileSystemModel()
t = TableModel()

Expected Behavior

No errors, or a better explanation of what is wrong.

Actual Behavior

error: Definition of "index" in base class "QAbstractItemModel" is incompatible with definition in base class "FileSystemModelProtocol" [misc]

Your Environment

• Mypy version used:
• mypy 1.9.0 (compiled: yes)
• Mypy command-line flags:
• none
• Mypy configuration options from mypy.ini (and other config files):
• none
• Python version used:
  Python 3.11.7
  PyQt6==6.6.1

Start by running the provided PyQt6 reproduction with mypy 1.9.0 and inspect how the overloaded index definitions are compared across QAbstractItemModel, QFileSystemModel, and the protocol. Compare the result with pyright and pytype as reported; done means the incompatibility is correctly handled or the diagnostic clearly explains the actual issue.