### 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
exiting = true;
	if (project_run_bar->is_playing()) {
		project_run_bar->stop_playing();
	}
	String to_reopen;
	if (get_tree()->get_edited_scene_root()) {
		to_reopen = get_tree()->get_edited_scene_root()->get_scene_file_path();
	}
	_exit_editor(EXIT_SUCCESS);
	List<String> args;
	for (const String &a : Main::get_forwardable_cli_arguments(Main::CLI_SCOPE_TOOL)) {
		args.push_back(a);
	}
	args.push_back("--path");
	args.push_back(ProjectSettings::get_singleton()->get_resource_path());
	args.push_back("-e");
	if (!to_reopen.is_empty()) {
		args.push_back(to_reopen);
	}
	OS::get_singleton()->set_restart_on_exit(true, args);
}
void EditorNode::_save_all_scenes() {