### 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
EditorNode::ExecuteThreadArgs *eta = (EditorNode::ExecuteThreadArgs *)p_ud;
	Error err = OS::get_singleton()->execute(eta->path, eta->args, &eta->output, &eta->exitcode, true, &eta->execute_output_mutex);
	print_verbose("Thread exit status: " + itos(eta->exitcode));
	if (err != OK) {
		eta->exitcode = err;
	}
	eta->done.set();
}
int EditorNode::execute_and_show_output(const String &p_title, const String &p_path, const List<String> &p_arguments, bool p_close_on_ok, bool p_close_on_errors, String *r_output) {
	if (execute_output_dialog) {
		execute_output_dialog->set_title(p_title);
		execute_output_dialog->get_ok_button()->set_disabled(true);
		execute_outputs->clear();
		execute_outputs->set_scroll_follow(true);
		EditorInterface::get_singleton()->popup_dialog_centered_ratio(execute_output_dialog);
	}
	ExecuteThreadArgs eta;
	eta.path = p_path;
	eta.args = p_arguments;
	eta.exitcode = 255;
	int prev_len = 0;
	eta.execute_output_thread.start(_execute_thread, &eta);