perf(tools): cache ToolRegistry.get_definitions() between mutations

get_definitions() sorts tools on every LLM iteration for prompt cache
stability.  Cache the sorted result and invalidate on register/unregister
so the sort only runs when the tool set actually changes.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

tests/tools/test_tool_registry.py

@@ -71,3 +71,33 @@ def test_prepare_call_other_tools_keep_generic_object_validation() -> None:
     assert tool is not None
     assert params == ["TODO"]
     assert error == "Error: Invalid parameters for tool 'grep': parameters must be an object, got list"
+
+
+def test_get_definitions_returns_cached_result() -> None:
+    registry = ToolRegistry()
+    registry.register(_FakeTool("read_file"))
+    first = registry.get_definitions()
+    assert registry._cached_definitions is not None
+    second = registry.get_definitions()
+    assert first == second
+
+
+def test_register_invalidates_cache() -> None:
+    registry = ToolRegistry()
+    registry.register(_FakeTool("read_file"))
+    first = registry.get_definitions()
+    registry.register(_FakeTool("write_file"))
+    second = registry.get_definitions()
+    assert first is not second
+    assert len(second) == 2
+
+
+def test_unregister_invalidates_cache() -> None:
+    registry = ToolRegistry()
+    registry.register(_FakeTool("read_file"))
+    registry.register(_FakeTool("write_file"))
+    first = registry.get_definitions()
+    registry.unregister("write_file")
+    second = registry.get_definitions()
+    assert first is not second
+    assert len(second) == 1