### 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
}
			}
		}
		
		List<Node::GroupInfo> groups;
		p_node->get_groups(&groups);
		if (!modified_properties.is_empty() || !valid_connections_to.is_empty() || !valid_connections_from.is_empty() || !groups.is_empty()) {
			ModificationNodeEntry modification_node_entry;
			modification_node_entry.property_table = modified_properties;
			modification_node_entry.connections_to = valid_connections_to;
			modification_node_entry.connections_from = valid_connections_from;
			modification_node_entry.groups = groups;
			p_modification_table[p_root->get_path_to(p_node)] = modification_node_entry;
		}
	} else {
		AdditiveNodeEntry new_additive_node_entry;
		new_additive_node_entry.node = p_node;
		new_additive_node_entry.parent = p_root->get_path_to(p_node->get_parent());
		new_additive_node_entry.owner = p_node->get_owner();
		new_additive_node_entry.index = p_node->get_index();
		Node2D *node_2d = Object::cast_to<Node2D>(p_node);
		if (node_2d) {
			new_additive_node_entry.transform_2d = node_2d->get_relative_transform_to_parent(node_2d->get_parent());
		}
		Node3D *node_3d = Object::cast_to<Node3D>(p_node);
		if (node_3d) {
			new_additive_node_entry.transform_3d = node_3d->get_relative_transform(node_3d->get_parent());
		}
		
		HashMap<Node *, Node *> ownership_table;