### 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
save_confirmation->set_text(TTR("Save modified resources before reloading?"));
						} else {
							save_confirmation->set_ok_button_text(TTR("Save & Quit"));
							save_confirmation->set_text(TTR("Save modified resources before closing?"));
						}
						save_confirmation->reset_size();
						save_confirmation->popup_centered();
						break;
					}
					plugin_to_save = nullptr;
					for (int i = 0; i < editor_data.get_editor_plugin_count(); i++) {
						const String unsaved_status = editor_data.get_editor_plugin(i)->get_unsaved_status();
						if (!unsaved_status.is_empty()) {
							if (p_option == RELOAD_CURRENT_PROJECT) {
								save_confirmation->set_ok_button_text(TTR("Save & Reload"));
								save_confirmation->set_text(unsaved_status);
							} else {
								save_confirmation->set_ok_button_text(TTR("Save & Quit"));
								save_confirmation->set_text(unsaved_status);
							}
							save_confirmation->reset_size();
							save_confirmation->popup_centered();
							plugin_to_save = editor_data.get_editor_plugin(i);
							break;
						}
					}
					if (plugin_to_save) {
						break;
					}
					_discard_changes();