Laravel 8 shows blank white screen on production server

So I am trying to run my Laravel 8 application on my server. I don't have root/SSH access, so I do everything with an FTP client. I uploaded all my content to my webserver and added my .htaccess file in order to run the application. It works fine in my local environment, but on my server it shows only a blank page. I put some debugging outputs in the public/index.php file and it can var_dump the $app variable.

$app = require_once __DIR__.'/../bootstrap/app.php';
var_dump($app); //Works

But I cannot var_dump $response.

$response = tap($kernel->handle(
    $request = Request::capture()
))->send();
var_dump($response); //Never reached statement

I guess it just aborts somewhere deep in the Laravel execution jungle and this would be hard to trace.

This is my project root .htaccess file:

<IfModule mod_rewrite.c>
    <IfModule mod_negotiation.c>
        Options -MultiViews -Indexes
    </IfModule>

    RewriteEngine On

    RewriteCond %{HTTP:Authorization} .
    RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]

    RewriteRule ^(.*)$ public/ [L,QSA]
</IfModule>

"public/$1" (seems to be not shown in the markdown...)

I cleared everythin in the storage folder but this doesnt make any impact. I also changed permissions of storage, vendor and bootstrap folder to 755 but it didn't change anything.

Locally it works both with php artisan serve or by placing everything in my htdocs folder of my XAMPP installation and browsing there.

What is the problem here?