Add anyset & frozenset, enable copying (cast) to std::set (#3901)

* Add frozenset, and allow it cast to std::set

For the reverse direction, std::set still casts to set. This is in concordance with the behavior for sequence containers, where e.g. tuple casts to std::vector but std::vector casts to list.

Extracted from #3886.

* Rename set_base to any_set to match Python C API

since this will be part of pybind11 public API

* PR: static_cast, anyset

* Add tests for frozenset

and rename anyset methods

* Remove frozenset default ctor, add tests

Making frozenset non-default constructible means that we need to adjust pyobject_caster to not require that its value is default constructible, by initializing value to a nil handle.  This also allows writing C++ functions taking anyset, and is arguably a performance improvement, since there is no need to allocate an object that will just be replaced by load.

Add some more tests, including anyset::empty, anyset::size, set::add and set::clear.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Add rationale to `pyobject_caster` default ctor

* Remove ineffectual protected: access control

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

tests/test_pytypes.py

@@ -66,11 +66,12 @@ def test_none(capture, doc):
 
 def test_set(capture, doc):
     s = m.get_set()
+    assert isinstance(s, set)
     assert s == {"key1", "key2", "key3"}
 
+    s.add("key4")
     with capture:
-        s.add("key4")
-        m.print_set(s)
+        m.print_anyset(s)
     assert (
         capture.unordered
         == """
@@ -81,12 +82,43 @@ def test_set(capture, doc):
     """
     )
 
-    assert not m.set_contains(set(), 42)
-    assert m.set_contains({42}, 42)
-    assert m.set_contains({"foo"}, "foo")
+    m.set_add(s, "key5")
+    assert m.anyset_size(s) == 5
 
-    assert doc(m.get_list) == "get_list() -> list"
-    assert doc(m.print_list) == "print_list(arg0: list) -> None"
+    m.set_clear(s)
+    assert m.anyset_empty(s)
+
+    assert not m.anyset_contains(set(), 42)
+    assert m.anyset_contains({42}, 42)
+    assert m.anyset_contains({"foo"}, "foo")
+
+    assert doc(m.get_set) == "get_set() -> set"
+    assert doc(m.print_anyset) == "print_anyset(arg0: anyset) -> None"
+
+
+def test_frozenset(capture, doc):
+    s = m.get_frozenset()
+    assert isinstance(s, frozenset)
+    assert s == frozenset({"key1", "key2", "key3"})
+
+    with capture:
+        m.print_anyset(s)
+    assert (
+        capture.unordered
+        == """
+        key: key1
+        key: key2
+        key: key3
+    """
+    )
+    assert m.anyset_size(s) == 3
+    assert not m.anyset_empty(s)
+
+    assert not m.anyset_contains(frozenset(), 42)
+    assert m.anyset_contains(frozenset({42}), 42)
+    assert m.anyset_contains(frozenset({"foo"}), "foo")
+
+    assert doc(m.get_frozenset) == "get_frozenset() -> frozenset"
 
 
 def test_dict(capture, doc):
@@ -302,6 +334,7 @@ def test_constructors():
         list: range(3),
         dict: [("two", 2), ("one", 1), ("three", 3)],
         set: [4, 4, 5, 6, 6, 6],
+        frozenset: [4, 4, 5, 6, 6, 6],
         memoryview: b"abc",
     }
     inputs = {k.__name__: v for k, v in data.items()}