[PyOV][25.3] Remove deprecated binary operations Node API (#30636)

### Blocked by:
- Currently blocked by the deprecated API usage in OpenVINO Keras
backend. This PR needs to be merged first:
keras-team/keras#21317

### Details:
- Originally deprecated in
#26761
- Fixed a test which before API removal was most likely doing an `assert
ops.Equal`, essentially checking `assert True`

### Tickets:
 - CVS-131039

---------

Signed-off-by: p-wysocki <przemyslaw.wysocki@intel.com>
Co-authored-by: Michal Lukaszewski <michal.lukaszewski@intel.com>

Author: p-wysocki

src/bindings/python/src/openvino/runtime/__init__.py

@@ -84,13 +84,3 @@
 # Helper functions for openvino module
 from openvino.runtime.ie_api import tensor_from_file
 from openvino.runtime.ie_api import compile_model
-
-from openvino.utils import deprecated
-
-# Extend Node class to support binary operators
-Node.__eq__ = deprecated(version="2025.3", message="Use ops.equal instead")(opset13.equal)
-Node.__ne__ = deprecated(version="2025.3", message="Use ops.not_equal instead")(opset13.not_equal)
-Node.__lt__ = deprecated(version="2025.3", message="Use ops.less instead")(opset13.less)
-Node.__le__ = deprecated(version="2025.3", message="Use ops.less_equal instead")(opset13.less_equal)
-Node.__gt__ = deprecated(version="2025.3", message="Use ops.greater instead")(opset13.greater)
-Node.__ge__ = deprecated(version="2025.3", message="Use ops.greater_equal instead")(opset13.greater_equal)

src/bindings/python/tests/test_runtime/test_deprecated_runtime.py

@@ -366,62 +366,3 @@ def test_runtime_passes_manager():
 
     assert count_ops_of_type(model, node_ceil) == 0
     assert count_ops_of_type(model, node_constant) == 1
-
-
-# from test_graph/test_ops_binary.py
-@pytest.mark.parametrize(
-    ("operator", "expected_type", "warning_type"),
-    [
-        (operator.add, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.sub, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.mul, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.truediv, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.eq, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.ne, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.gt, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.ge, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.lt, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.le, Type.boolean, pytest.warns(DeprecationWarning)),
-    ],
-)
-def test_binary_operators(operator, expected_type, warning_type):
-    value_b = np.array([[4, 5], [1, 7]], dtype=np.float32)
-
-    shape = [2, 2]
-    parameter_a = ops.parameter(shape, name="A", dtype=np.float32)
-
-    with warning_type:
-        model = operator(parameter_a, value_b)
-
-    assert model.get_output_size() == 1
-    assert list(model.get_output_shape(0)) == shape
-    assert model.get_output_element_type(0) == expected_type
-
-
-@pytest.mark.parametrize(
-    ("operator", "expected_type", "warning_type"),
-    [
-        (operator.add, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.sub, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.mul, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.truediv, Type.f32, warnings.catch_warnings(record=True)),
-        (operator.eq, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.ne, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.gt, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.ge, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.lt, Type.boolean, pytest.warns(DeprecationWarning)),
-        (operator.le, Type.boolean, pytest.warns(DeprecationWarning)),
-    ],
-)
-def test_binary_operators_with_scalar(operator, expected_type, warning_type):
-    value_b = np.array([[5, 6], [7, 8]], dtype=np.float32)
-
-    shape = [2, 2]
-    parameter_a = ops.parameter(shape, name="A", dtype=np.float32)
-
-    with warning_type:
-        model = operator(parameter_a, value_b)
-
-    assert model.get_output_size() == 1
-    assert list(model.get_output_shape(0)) == shape
-    assert model.get_output_element_type(0) == expected_type

src/bindings/python/tests/test_transformations/test_replacement_api.py

@@ -52,11 +52,14 @@ def test_replace_node():
 
 
 def test_replace_output_update_name():
+    # Before replacement: param -> relu -> exp -> result
+    # After replacement: param -> relu -> result
     param = ops.parameter(PartialShape([1, 3, 22, 22]), name="parameter")
     relu = ops.relu(param.output(0))
     exp = ops.exp(relu.output(0))
     res = ops.result(exp.output(0), name="result")
 
     replace_output_update_name(exp.output(0), exp.input_value(0))
 
-    assert res.input_value(0).get_node() == exp
+    assert res.input_value(0).get_node().get_instance_id() == relu.get_instance_id()
+    assert res.input_value(0).get_node().get_friendly_name() == exp.get_friendly_name()