Logo is not sharp

Why do you use an image for that?
use svg for that (by the way what font was that )

you can allow the mime-type svg via child-theme functions.php :

function custom_mtypes( $m ){
    $m['svg'] = 'image/svg+xml';
    $m['svgz'] = 'image/svg+xml';
    return $m;
}
add_filter( 'upload_mimes', 'custom_mtypes' );

or my recommendation is to use that very nice little plugin svg-support

then you even can use svg inline – not as img src
there are some css you had to place then – because not all svgs have height – width definitions inside.
so f.e a width in absolut value had to be set for some browsers.

The plugin only has the possibility to replace the img tag with inline svg whereever you like it.
First of all: There is a lot of crap in that svg ( if i create a svg file with illustrator – there is only the creator on top
The thing is that there is a possibility to test this without the plugin via via child-theme functions.php with:

// insert svg as logo
function replace_logo_with_svg() {
?>
  <script type="text/javascript">
  (function($) {
    function a() {
      $( ".logo a img" ).remove();
      $.get('http://00247-01.htz-cs06.clickstorm.de/wp-content/uploads/2020/02/EASH-Verlagsgruppe2.svg', function(svg){
        $( ".logo a" ).html( svg );
      }, 'text');
    }
    a();
  })(jQuery);
  </script>
<?php
}
add_action('wp_footer', 'replace_logo_with_svg');

But with your svg there is a lot of additonal unnecessary informations in it ( adobe things – some image relicts etc. pp)
your svg is not set to responsive behavior. i put in the svg code : preserveAspectRatio="xMinYMid meet" etc. pp
look into this svg code ( open with good text-editor like sublime-text on mac or notepad++ on pc or similar ) : https://webers-testseite.de/EASH-Verlagsgruppe2.svg

if you use that as svg you even don’t need a transparency extra logo – you can fill the paths with a different color on this case:

.logo a {
  display: inline-flex;
}

.av_header_transparency .logo svg .sh0 {
  fill: #fff;
  transition: all 0.7s ease
}