### 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
immediate_dialog_confirmed = true;
}
bool EditorNode::immediate_confirmation_dialog(const String &p_text, const String &p_ok_text, const String &p_cancel_text, uint32_t p_wrap_width) {
	ConfirmationDialog *cd = memnew(ConfirmationDialog);
	cd->set_text(p_text);
	cd->set_ok_button_text(p_ok_text);
	cd->set_cancel_button_text(p_cancel_text);
	if (p_wrap_width > 0) {
		cd->set_autowrap(true);
		cd->get_label()->set_custom_minimum_size(Size2(p_wrap_width, 0) * EDSCALE);
	}
	cd->connect("confirmed", callable_mp(singleton, &EditorNode::_immediate_dialog_confirmed));
	singleton->gui_base->add_child(cd);
	cd->popup_centered();
	while (true) {
		OS::get_singleton()->delay_usec(1);
		DisplayServer::get_singleton()->process_events();
		Main::iteration();
		if (singleton->immediate_dialog_confirmed || !cd->is_visible()) {
			break;
		}
	}
	memdelete(cd);
	return singleton->immediate_dialog_confirmed;
}
void EditorNode::cleanup() {