[BUG]: `tp_name` field not initialized correctly for a nested class

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What version (or hash if on master) of pybind11 are you using?

2.11.1

Problem description

Consider the following bindings for a class Pet and some nested class Pet.Attributes, whichs is taken from the pybind11 docs:

py::class_<Pet> pet(m, "Pet");

py::class_<Pet::Attributes>(pet, "Attributes")
    .def(py::init<>());

pybind11 seems to be computing a wrong tp_name field for the nested class' PyTypeObject in make_new_python_type(). The class ends up being named just mymodule.Attributes instead of the expected mymodule.Pet.Attributes.

This can be demonstrated: The Python interpreter uses the wrong tp_name in error messages, for example:

import mymodule
a = mymodule.Pet.Attributes()
print(a.nonexisting)

gives the following error string:

AttributeError: 'mymodule.Attributes' object has no attribute 'nonexisting'

Please let me know if you also think this needs to be fixed. If so, I would be willing to contribute a pull request.

Reproducible example code

No response

Is this a regression? Put the last known working version here if it is.

Not a regression

Start in include/pybind11/detail/class.h at make_new_python_type(), then reproduce the nested Pet.Attributes case described in the issue and inspect the generated PyTypeObject name. Done means Python errors identify the object as mymodule.Pet.Attributes rather than mymodule.Attributes.