### 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
}
		} else if (current_res->get_path().is_resource_file()) {
			if (FileAccess::exists(current_res->get_path() + ".import")) {
				editable_info = TTR("This resource was imported, so it's not editable. Change its settings in the import panel and then re-import.");
			}
		}
	} else if (is_node) {
		Node *current_node = Object::cast_to<Node>(current_obj);
		ERR_FAIL_NULL(current_node);
		InspectorDock::get_inspector_singleton()->edit(current_node);
		if (current_node->is_inside_tree()) {
			NodeDock::get_singleton()->set_node(current_node);
			SceneTreeDock::get_singleton()->set_selected(current_node);
			InspectorDock::get_singleton()->update(current_node);
			if (!inspector_only && !skip_main_plugin) {
				skip_main_plugin = stay_in_script_editor_on_node_selected && !ScriptEditor::get_singleton()->is_editor_floating() && ScriptEditor::get_singleton()->is_visible_in_tree();
			}
		} else {
			NodeDock::get_singleton()->set_node(nullptr);
			SceneTreeDock::get_singleton()->set_selected(nullptr);
			InspectorDock::get_singleton()->update(nullptr);
		}
		if (get_edited_scene() && !get_edited_scene()->get_scene_file_path().is_empty()) {
			String source_scene = get_edited_scene()->get_scene_file_path();
			if (FileAccess::exists(source_scene + ".import")) {
				editable_info = TTR("This scene was imported, so changes to it won't be kept.\nInstantiating or inheriting it will allow you to make changes to it.\nPlease read the documentation relevant to importing scenes to better understand this workflow.");
				info_is_warning = true;
			}
		}
	} else {