Pure pybind example of overload failure

tmp/BUILD.bazel

@@ -0,0 +1,14 @@
+load("//tools/skylark:pybind.bzl", "pybind_py_library")
+
+pybind_py_library(
+    name = "cc_py",
+    cc_so_name = "cc",
+    cc_srcs = ["cc_py.cc"],
+    py_imports = ["."],
+)
+
+py_test(
+    name = "cc_py_test",
+    srcs = ["cc_py_test.py"],
+    deps = [":cc_py"],
+)

tmp/cc_py.cc

@@ -0,0 +1,54 @@
+#include "pybind11/eigen.h"
+#include "pybind11/pybind11.h"
+
+namespace py = pybind11;
+
+namespace drake {
+
+struct MyScalar {
+  int value{};
+};
+
+}  // namespace drake
+
+PYBIND11_NUMPY_OBJECT_DTYPE(drake::MyScalar);
+
+namespace drake {
+namespace {
+
+std::string AcceptMatrixDense(const Eigen::MatrixXd&) {
+  return "dense";
+}
+
+std::string AcceptMatrixSparse(const Eigen::SparseMatrix<double>&) {
+  return "sparse";
+}
+
+using VectorXMyScalar = Eigen::Matrix<MyScalar, Eigen::Dynamic, 1>;
+
+std::string AcceptMatrixAndObjectDense(
+    const Eigen::MatrixXd&, const VectorXMyScalar&) {
+  return "dense";
+}
+
+std::string AcceptMatrixAndObjectSparse(
+    const Eigen::SparseMatrix<double>&, const VectorXMyScalar&) {
+  return "sparse";
+}
+
+// Try to replicate signature as in #20516.
+
+PYBIND11_MODULE(cc, m) {
+  m.def("AcceptMatrix", &AcceptMatrixDense);
+  m.def("AcceptMatrix", &AcceptMatrixSparse);
+
+  py::class_<MyScalar>(m, "MyScalar")
+      .def(py::init<int>(), py::arg("value"))
+      .def_readwrite("value", &MyScalar::value);
+
+  m.def("AcceptMatrixAndObject", &AcceptMatrixAndObjectSparse);
+  m.def("AcceptMatrixAndObject", &AcceptMatrixAndObjectDense);
+}
+
+}  // namespace
+}  // namespace drake

tmp/cc_py_test.py

@@ -0,0 +1,23 @@
+import unittest
+
+import numpy as np
+import scipy.sparse
+
+from drake.tmp.cc import AcceptMatrix, AcceptMatrixAndObject, MyScalar
+
+
+class Test(unittest.TestCase):
+    def test_overload(self):
+        A_dense = np.eye(2)
+        A_sparse = scipy.sparse.csc_matrix(np.eye(2))
+        self.assertEqual(AcceptMatrix(A_dense), "dense")
+        self.assertEqual(AcceptMatrix(A_sparse), "sparse")
+
+        x = np.array([MyScalar(1), MyScalar(2)])
+        self.assertEqual(x.dtype, object)
+        self.assertEqual(AcceptMatrixAndObject(A_dense, x), "dense")
+        self.assertEqual(AcceptMatrixAndObject(A_sparse, x), "sparse")
+
+
+if __name__ == "__main__":
+    unittest.main()