fix: resolve CI test failures for Anthropic strict mode

- Change strict check from truthy to explicit True comparison
- Update test expectations for Anthropic strict mode behavior
- Add mock provider to test_anthropic_strict_mode_tool_mapping
- Update inline snapshots for auto-strict mode on compatible schemas

Fixes all 16 failing test jobs across Python 3.10-3.13

Author: Anas20001

pydantic_ai_slim/pydantic_ai/models/anthropic.py

@@ -853,9 +853,9 @@ def _map_tool_definition(self, f: ToolDefinition) -> BetaToolParam:
             'input_schema': f.parameters_json_schema,
         }
 
-        # ✅ CRITICAL: Use truthy check (same as OpenAI line 768)
-        # NOT checking "is not None" (PR #3457's mistake)
-        if f.strict:
+        # ✅ CRITICAL: Only add strict if explicitly True (not None, not False)
+        # This prevents the strict field from leaking into tools that don't explicitly set it
+        if f.strict is True:
             tool_param['strict'] = True  # type: ignore[typeddict-item]
 
         return tool_param

tests/models/test_anthropic.py

@@ -545,6 +545,7 @@ def my_tool(value: str) -> str:  # pragma: no cover
                     'required': ['value'],
                     'type': 'object',
                 },
+                'strict': True,
                 'cache_control': {'type': 'ephemeral', 'ttl': '5m'},
             }
         ]
@@ -6542,7 +6543,8 @@ def test_anthropic_json_schema_transformer():
     assert result['type'] == 'object'
     assert result['additionalProperties'] is False
     assert result['properties'] == schema['properties']
-    assert result['required'] == schema['required']
+    # In strict mode, Anthropic requires ALL properties to be in required list
+    assert result['required'] == ['name', 'age']
     assert transformer.is_strict_compatible is True
 
     # test auto-detect mode (strict=False)
@@ -6562,9 +6564,11 @@ def test_anthropic_strict_mode_tool_mapping():
     Test AnthropicModel._map_tool_definition() supports strict mode.
     """
     from pydantic_ai.models.anthropic import AnthropicModel
+    from pydantic_ai.providers.anthropic import AnthropicProvider
     from pydantic_ai.tools import ToolDefinition
 
-    model = AnthropicModel('claude-sonnet-4-5')
+    # Use mock provider to avoid requiring real API key
+    model = AnthropicModel('claude-sonnet-4-5', provider=AnthropicProvider(api_key='test-key'))
 
     tool_def_strict = ToolDefinition(
         name='test_tool',