### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
HashMap<StringName, Variant> modified_property_map;
	List<PropertyInfo> pinfo;
	p_node->get_property_list(&pinfo);
	for (const PropertyInfo &E : pinfo) {
		if (E.usage & PROPERTY_USAGE_STORAGE) {
			bool is_valid_revert = false;
			Variant revert_value = EditorPropertyRevert::get_property_revert_value(p_node, E.name, &is_valid_revert);
			Variant current_value = p_node->get(E.name);
			if (is_valid_revert) {
				if (PropertyUtils::is_property_value_different(current_value, revert_value)) {
					modified_property_map[E.name] = current_value;
				}
			}
		}
	}
	return modified_property_map;
}
void EditorNode::update_ownership_table_for_addition_node_ancestors(Node *p_current_node, HashMap<Node *, Node *> &p_ownership_table) {
	p_ownership_table.insert(p_current_node, p_current_node->get_owner());
	for (int i = 0; i < p_current_node->get_child_count(); i++) {
		Node *child = p_current_node->get_child(i);
		update_ownership_table_for_addition_node_ancestors(child, p_ownership_table);
	}
}
void EditorNode::update_diff_data_for_node(