register_exception does not work after re-initializing an embedded interpreter

Consider the following example, which adds an exception type SomeException to module foo , re-initializes the interpreter, and tries to do the same again:

PYBIND11_EMBEDDED_MODULE(foo, mod) { /* Nothing */ }

struct SomeException : public std::runtime_error {};

int main() {

    {
        pybind11::scoped_interpreter interpreter;
        auto foo = pybind11::module::import("foo");
        pybind11::register_exception<SomeException>(foo, "SomeException");
        assert(!foo.attr("SomeException").is_none());
    }

    {
        pybind11::scoped_interpreter interpreter;
        auto foo = pybind11::module::import("foo");
        pybind11::register_exception<SomeException>(foo, "SomeException");
        assert(!foo.attr("SomeException").is_none()); // This throws an exception
    }

}

The second call to register_exception fails silently, because the first pybind11::exception object is still alive due to its static lifetime in pybind11::detail::get_exception_object, making register_exception think that the type has already been added.

The same behavior can be observed when trying to add the same exception type to multiple modules:

PYBIND11_EMBEDDED_MODULE(foo, mod) { /* Nothing */ }
PYBIND11_EMBEDDED_MODULE(bar, mod) { /* Nothing */ }

struct SomeException : public std::runtime_error {};

int main() {
    pybind11::scoped_interpreter interpreter;
    auto foo = pybind11::module::import("foo");
    pybind11::register_exception<SomeException>(foo, "SomeException");
    pybind11::register_exception<SomeException>(bar, "SomeException");
    assert(!foo.attr("SomeException").is_none());
    assert(!bar.attr("SomeException").is_none()); // This throws an exception
}

Start in include/pybind11/pybind11.h at detail::get_exception_object, which the issue identifies as retaining the exception object across interpreter lifetimes. Reproduce the examples for interpreter re-initialization and registration in multiple modules; done means both calls expose SomeException without throwing or silently failing.