Exposing `std::variant` as `TypeAlias` with Pybind11

I'm curious if there's a way to avoid repeating myself. I have several classes that are not related by parentage:

#include <pybind11/operators.h>
#include <pybind11/pybind11.h>
#include <pybind11/stl.h>

namespace py = pybind11;

class Foo {
  public:
    Foo(int x)
        : x(x)
    {}

    int x;
};

class Bar {
  public:
    Bar(int y)
        : y(y)
    {}

    int y;
};

using FooBarType = std::variant<Foo, Bar>;

PYBIND11_MODULE(my_module, m)
{
    py::class_<Foo>(m, "Foo")
        .def(py::init<int>())
        .def_readwrite("x", &Foo::x);

    py::class_<Bar>(m, "Bar")
        .def(py::init<int>())
        .def_readwrite("y", &Bar::y);
}

And my Python code:

from typing import TypeAlias

from my_moduleimport Foo, Bar

FooBarType: TypeAlias = Foo | Bar

def check_foo_bar(value: FooBarType, expected: int):
    if isinstance(value, Foo):
        assert value.x == expected
    elif isinstance(value, Bar):
        assert value.y == expected
    else:
        raise ValueError(f"Unknown type: {type(value)}")

def test_foo_bar():
    foo: FooBarType = Foo(1)
    bar: FooBarType = Bar(2)
    check_foo_bar(foo, 1)
    check_foo_bar(bar, 2)

I'm trying to create a binding to using FooBarType = std::variant<Foo, Bar> so I don't have to define FooBarType: TypeAlias = Foo | Bar.

I've tried using pybind11::type::of:

m.def("FooBarType", py::type::of<FooBarType>());

But that blows up with

In file included from test.cpp:4:
In file included from /home/user/work/external/pybind11/include/pybind11/operators.h:12:
In file included from /home/user/work/external/pybind11/include/pybind11/pybind11.h:13:
In file included from /home/user/work/external/pybind11/include/pybind11/detail/class.h:12:
In file included from /home/user/work/external/pybind11/include/pybind11/attr.h:14:
/home/user/work/external/pybind11/include/pybind11/cast.h:1646:5: error: static_assert failed due to requirement 'std::is_base_of<pybind11::detail::type_caster_generic, pybind11::detail::type_caster<std::variant<Foo, Bar>, void>>::value' "py::type::of<T> only supports the case where T is a registered C++ types."
    static_assert(std::is_base_of<detail::type_caster_generic, detail::make_caster<T>>::value,
    ^             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/user/work/external/pybind11/include/pybind11/pytypes.h:1392:27: note: in instantiation of function template specialization 'pybind11::type::handle_of<std::variant<Foo, Bar>>' requested here
        return type(type::handle_of<T>(), borrowed_t{});
                          ^
test.cpp:125:35: note: in instantiation of function template specialization 'pybind11::type::of<std::variant<Foo, Bar>>' requested here
    m.def("FooBarType", py::type::of<FooBarType>());
                                  ^
In file included from test.cpp:4:
In file included from /home/user/work/external/pybind11/include/pybind11/operators.h:12:
In file included from /home/user/work/external/pybind11/include/pybind11/pybind11.h:13:
In file included from /home/user/work/external/pybind11/include/pybind11/detail/class.h:12:
In file included from /home/user/work/external/pybind11/include/pybind11/attr.h:13:
/home/user/work/external/pybind11/include/pybind11/detail/common.h:867:49: error: reference to overloaded function could not be resolved; did you mean to call it?
    using type = typename remove_class<decltype(&F::operator())>::type;

Any help is appreciated.

Cheers!