[BUG]: Coverity warning: Uncaught exceptions

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

2.11.1

Problem description

There is a report made for pytypes.h:

CID 323117 (#1 of 1): Uncaught exception (UNCAUGHT_EXCEPT)
exn_spec_violation: An exception of type std::runtime_error is thrown but the
exception specification noexcept doesn't allow it to be thrown. This will result in a call to terminate().
387    object &operator=(object &&other) noexcept {
388        if (this != &other) {
389            handle temp(m_ptr);
390            m_ptr = other.m_ptr;
391            other.m_ptr = nullptr;
   fun_call_w_exception: Called function dec_ref throws an exception of type std::runtime_error. [show details]
392            temp.dec_ref();
393        }
394        return *this;
395    }

267 const handle &dec_ref() const & {
268#ifdef PYBIND11_ASSERT_GIL_HELD_INCREF_DECREF
269        if (m_ptr != nullptr && !PyGILState_Check()) {
   1. fun_call_w_exception: Called function throw_gilstate_error throws an exception of type std::runtime_error.
270            throw_gilstate_error("pybind11::handle::dec_ref()");
271        }
272#endif
273        Py_XDECREF(m_ptr);
274        return *this;
275    }

301    void throw_gilstate_error(const std::string &function_name) const {
302        fprintf(
303            stderr,
304            "%s is being called while the GIL is either not held or invalid. Please see "
305            "https://pybind11.readthedocs.io/en/stable/advanced/"
306            "misc.html#common-sources-of-global-interpreter-lock-errors for debugging advice.\n"
307            "If you are convinced there is no bug in your code, you can #define "
308            "PYBIND11_NO_ASSERT_GIL_HELD_INCREF_DECREF"
309            "to disable this check. In that case you have to ensure this #define is consistently "
310            "used for all translation units linked into a given pybind11 extension, otherwise "
311            "there will be ODR violations.",
312            function_name.c_str());
313        fflush(stderr);
314        if (Py_TYPE(m_ptr)->tp_name != nullptr) {
315            fprintf(stderr,
316                    "The failing %s call was triggered on a %s object.\n",
317                    function_name.c_str(),
318                    Py_TYPE(m_ptr)->tp_name);
319            fflush(stderr);
320        }
   1. exception_thrown: An exception of type std::runtime_error is thrown.
321        throw std::runtime_error(function_name + " PyGILState_Check() failure.");
322    }

Reproducible example code

No response

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

Not a regression

Start in pytypes.h at object::operator=(object&&), then trace handle::dec_ref() and throw_gilstate_error() under PYBIND11_ASSERT_GIL_HELD_INCREF_DECREF. The issue provides no reproducible example or test file; done means addressing the Coverity uncaught-exception report without breaking the GIL assertion behavior.