[bindings] Update memory leak test

Convert the test to unittest format, rewrite the instrumentation, and
track the current numbers of leaks, with the goal of reaching 0 once
fixes are landed.

As leaks are fixed, the test will complain about allowing more leaks
than actually occurred, prompting update or removal of the leaks
allowed.

bindings/pydrake/BUILD.bazel

@@ -392,20 +392,14 @@ drake_py_unittest(
  tags = ["lint"],
 )
 
-# TODO(jwnimmer-tri) Once this a real test, switch it to drake_py_unittest.
-drake_py_binary(
+drake_py_unittest(
  name = "memory_leak_test",
- srcs = ["test/memory_leak_test.py"],
- add_test_rule = True,
  data = [
  "@drake_models//:iiwa_description",
  "@drake_models//:manipulation_station",
  "@drake_models//:veggies",
  "@drake_models//:wsg_50_description",
  ],
- test_rule_args = [
- "--count=2",
- ],
  deps = [
  ":all_py",
  ],