### 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
break;
				}
				if (save_each) {
					tab_closing_menu_option = current_menu_option;
					for (int i = 0; i < editor_data.get_edited_scene_count(); i++) {
						tabs_to_close.push_back(editor_data.get_scene_path(i));
					}
					_proceed_closing_scene_tabs();
				} else {
					String unsaved_scenes;
					int i = _next_unsaved_scene(true, 0);
					while (i != -1) {
						unsaved_scenes += "\n            " + editor_data.get_edited_scene_root(i)->get_scene_file_path();
						i = _next_unsaved_scene(true, ++i);
					}
					if (p_option == RELOAD_CURRENT_PROJECT) {
						save_confirmation->set_ok_button_text(TTR("Save & Reload"));
						save_confirmation->set_text(TTR("Save changes to the following scene(s) before reloading?") + unsaved_scenes);
					} else {
						save_confirmation->set_ok_button_text(TTR("Save & Quit"));
						save_confirmation->set_text((p_option == FILE_QUIT ? TTR("Save changes to the following scene(s) before quitting?") : TTR("Save changes to the following scene(s) before opening Project Manager?")) + unsaved_scenes);
					}
					save_confirmation->reset_size();
					save_confirmation->popup_centered();
				}
				DisplayServer::get_singleton()->window_request_attention();
				break;
			}
			_save_external_resources();
			_discard_changes();