[BUG]: TypeError raised on C++ integer overflow during type conversion

Required prerequisites

• Make sure you've read the documentation. Your issue may be addressed there.
• Search the issue tracker and Discussions to verify that this hasn't already been reported. +1 or comment there if it has.
• Consider asking first in the Gitter chat room or in a Discussion.

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

2.10.4

Problem description

When passing a python integer to a C++ function, if the Python integer overflows the C++ integer, pybind11 raises TypeError.

For parity with the CPython interpreter, the best exception to raise would probably be the OverflowError as this is the exception raised by PyLong_As* family of functions provided by the CPython stable ABI.

Reproducible example code

//C++ code
#include <iostream>
#include <cstdint>

#include <pybind11/pybind11.h>

namespace py = pybind11;

int64_t int_overflow64(int64_t a) {
    return a;
}

int32_t int_overflow32(int32_t a) {
    return a;
}

int16_t int_overflow16(int16_t a) {
    return a;
}

int8_t int_overflow8(int8_t a) {
    return a;
}

void overflow_test(py::int_ i){
    const long value = PyLong_AsLong(i.ptr());
    if (PyErr_Occurred()){
        throw py::error_already_set();
    }
}

PYBIND11_MODULE(overflowExample, m) {
    m.def("int_overflow64", &int_overflow64, "");
    m.def("int_overflow32", &int_overflow32, "");
    m.def("int_overflow16", &int_overflow16, "");
    m.def("int_overflow8", &int_overflow8, "");
    m.def("overflow_test", &overflow_test, "");
}


# Python Code:
import overflowExample
overflowExample.int_overflow64(9999999999999) # Type Error
overflowExample.int_overflow32(9999999999999) # Type Error
overflowExample.int_overflow16(9999999999999) # Type Error
overflowExample.int_overflow8(9999999999999)  # Type Error
overflowExample.overflow_test(9999999999999)  # Overflow Error

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

Not a regression

Start by running the supplied C++/Python reproducer, especially int_overflow64, int_overflow32, int_overflow16, int_overflow8, and overflow_test, and compare their exception types. Trace the integer conversion path used by those entry points; done means overflowing conversions raise OverflowError consistently with PyLong_As* behavior.