### 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
}
					
					for (KeyValue<Node *, Node *> &E : additive_node_entry.ownership_table) {
						Node *current_ancestor = E.key;
						Node *ancestor_owner = E.value;
						if (ancestor_owner == original_node) {
							ancestor_owner = instantiated_node;
						}
						current_ancestor->set_owner(ancestor_owner);
					}
				}
				
				if (selected_node_paths.size()) {
					for (NodePath selected_node_path : selected_node_paths) {
						Node *selected_node = instantiated_node->get_node_or_null(selected_node_path);
						if (selected_node) {
							editor_selection->add_node(selected_node);
						}
					}
					editor_selection->update();
				}
				
				for (KeyValue<NodePath, ModificationNodeEntry> &E : modification_table) {
					NodePath new_current_path = E.key;
					Node *modifiable_node = instantiated_node->get_node_or_null(new_current_path);
					if (modifiable_node) {
						
						List<PropertyInfo> pinfo;
						modifiable_node->get_property_list(&pinfo);