[BUG]: type_caster<std::complex<T>>'s parameter annotation omits builtin `complex` for Python 3.10

[IvanaGyro]

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

3.0.2~3.0.4

Problem description

Summary

pybind11/complex.h's type_caster<std::complex<T>> uses io_name(input, output) with two different annotation strings:

PYBIND11_TYPE_CASTER(
    std::complex<T>,
    io_name("typing.SupportsComplex | typing.SupportsFloat | typing.SupportsIndex",
            "complex"));

The output (return type) annotation is correctly complex. The input (parameter type) annotation is typing.SupportsComplex | typing.SupportsFloat | typing.SupportsIndex -- it does not include plain complex.

This is a real gap under strict type checking: typeshed's builtin complex type only gained __complex__ in Python >= 3.11 (see python/typeshed). Under Python 3.10 (still within pybind11's declared support window and a common requires-python floor for downstream projects), complex does not satisfy typing.SupportsComplex, so a stub generated from this caster rejects a call like f(2+1j) even though the C++ binding accepts it perfectly fine at runtime (the caster's load() uses PyComplex_AsCComplex, which handles a plain Python complex directly).

Reproduction

Any pybind11-bound function taking a std::complex<double>/std::complex<float> parameter, with a stub generated via pybind11-stubgen, produces a parameter annotation that a strict type checker (mypy/pyright under Python 3.10) rejects for a plain Python complex literal:

def f(z: typing.SupportsComplex | typing.SupportsFloat | typing.SupportsIndex) -> complex: ...

f(2 + 1j)  # type-checker error under Python 3.10: complex has no __complex__

Suggested fix

Prefix the input annotation with complex |, matching the output annotation's correctness:

io_name("complex | typing.SupportsComplex | typing.SupportsFloat | typing.SupportsIndex",
        "complex")

Reproducible example code

#include <complex>

#include <pybind11/complex.h>
#include <pybind11/pybind11.h>

namespace py = pybind11;

std::complex<double> ident(std::complex<double> z) {
    return z;
}

PYBIND11_MODULE(complex_issue, m) {
    m.def("ident", &ident);
}

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

3.0.1