I don't completly follow but if you are going to use switch, you need break before you define a new case, like this

switch (n) {
    case label1:
        code to be executed if n=label1;
        break;
    case label2:
        code to be executed if n=label2;
        break;
    case label3:
        code to be executed if n=label3;
        break;
    ...
    default:
        code to be executed if n is different from all labels;
}

In your controller method you pass the display mode to the template:

public function index()
{
        ...

        return view('index', [
            'displayMode' => $displayMode
        ]);
}

Blade does not support any switch statement. So you better use if-else-statements or plain PHP. For plain PHP @muppbarn already gave a good example.