### 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
ERR_FAIL_NULL_V(p_object, false);
	Ref<Script> scr = p_object->get_script();
	if (scr.is_null() && Object::cast_to<Script>(p_object)) {
		scr = p_object;
	}
	if (scr.is_valid()) {
		Ref<Script> base_script = scr;
		while (base_script.is_valid()) {
			StringName name = EditorNode::get_editor_data().script_class_get_name(base_script->get_path());
			if (name == p_class) {
				return true;
			}
			base_script = base_script->get_base_script();
		}
	}
	return false;
}
void EditorNode::progress_add_task(const String &p_task, const String &p_label, int p_steps, bool p_can_cancel) {
	if (singleton->cmdline_export_mode) {
		print_line(p_task + ": begin: " + p_label + " steps: " + itos(p_steps));
	} else if (singleton->progress_dialog) {
		singleton->progress_dialog->add_task(p_task, p_label, p_steps, p_can_cancel);
	}
}
bool EditorNode::progress_task_step(const String &p_task, const String &p_state, int p_step, bool p_force_refresh) {