How to include js- and php- code in layout properly via Assets in Yii2?

In your case it will be better to use $depends property in your AppAsset instead of extending the GlobalAppAsset.

You can leave GlobalAppAsset as is and the AppAsset should look like this:

class AppAsset extends AssetBundle
{
    //... other app assets configuration

    public $jsOptions = ['position' => \yii\web\View::POS_BEGIN];
    public $depends = [
        //... some other dependencies
        \fully\qualified\GlobalAppAsset::class
    ];
}

As for including the noscript snippet the assets are not a best way how to do that. There might be some way, for example overriding the register() method to register yii\web\View::EVENT_BEGIN_BODY then outputing the snippet in the registered event handler.

class GlobalAppAsset extends AssetBundle
{
    public $basePath = '@webroot';
    public $baseUrl = '@web';

    public $js = [
        'js/gtag_script1.js',
        'js/gtag_script2.js',
    ];

    public $jsOptions = ['position' => \yii\web\View::POS_HEAD];

    public static function register($view) {
        parent::register($view);
        $view->on(
            \yii\web\View::EVENT_BEGIN_BODY,
            function($event) use ($view) {
                echo $view->render('the-view-with-noscript');
            }
        )
    }
}

This solution might work but because this solution is not exactly standard it might cause issues with maintaining the code later.

The better solution for that would be using a widget but you will need to run the widget in each of your layout files.