// register Widget Area 
function register_logo_widget_area() {
  register_sidebar(array(
    'name'          => 'Logo Widget Area',
    'id'            => 'logo_widget_area',
    'description'   => 'Widget Area im Logo Container',
    'before_widget' => '<section id="%1$s" class="widget clearfix %2$s">', 
    'after_widget'  => '</section>', 
    'before_title'  => '<h3 class="widgettitle">', 
    'after_title'   => '</h3>',
  ));
}
add_action( 'widgets_init', 'register_logo_widget_area', 1001 );

// Insert widget area as sibling to anchor
function kriesi_logo_final_output($logo, $use_image, $headline_type, $sub, $alt, $link, $title) {

  // Filter only for some page-ids - here only that one page
  if (! is_page(array(54349))) {
    return $logo;
  }

  $logo_tag = 'div'; 
  
  if ( is_active_sidebar( 'logo_widget_area' ) ) {
    ob_start();
    dynamic_sidebar( 'logo_widget_area' );
    $widget_content = ob_get_clean();
    
    $logo = str_replace( '<' . $headline_type, '<' . $logo_tag, $logo);
    $logo = str_replace('</' . $headline_type . '>', $widget_content . '</' . $logo_tag . '>', $logo);
  } else {
    $logo = str_replace( '<' . $headline_type, '<' . $logo_tag, $logo);
    $logo = str_replace('</' . $headline_type . '>', '</' . $logo_tag . '>', $logo);
  }
  
  return $logo;
}
add_filter('avf_logo_final_output', 'kriesi_logo_final_output', 10, 7);

css setting

#top .logo {
  display: flex;
  flex-flow: row nowrap;
  justify-content: space-between; /* flex-start for widget-area next to logo */
  align-content: center;
  align-items: center;
  gap: 20px;
  width: 100% !important
}

#top .logo > a {
  display: flex;
  align-items: center;
  flex-shrink: 1;
}

#top .logo .widget {
  display: flex;
  flex-direction: column;
  justify-content: center;
  align-items: flex-start;
  align-self: center;
  padding: 0 !important;
  height: inherit;
  line-height: initial;
}

#top .logo .widget:before,
#top .logo .widget:after {
  display: none !important;
}

.html_header_top.html_bottom_nav_header #header_main_alternate .main_menu .menu-item-search-dropdown {
  float: left; 
}


.html_header_top.html_bottom_nav_header #header_main_alternate .main_menu {
  width: auto;
  left: 50%;
  transform: translateX(-50%);
}


#top .logo .widget .widgettitle {
  padding: 5px 0;
  margin-bottom: 5px
}


@media only screen and (max-width: 989px) {
  .responsive #top #wrap_all #header .container {
    width: 95%;
    max-width: 95%;
  }
  #top .logo .widget {
    align-items: flex-start;
  }
  .responsive #top #header_main > .container .main_menu .av-main-nav > li > a {
    line-height: 80px !important;
    height: 80px !important;
  }
}

@media only screen and (min-width: 768px ) and (max-width: 989px) {
  #top .logo {
    display: grid !important;
    grid-template-columns: 1fr 1fr;
    width: calc(100% - 80px) !important;
    justify-content: flex-start;
  }
}


@media only screen and (max-width: 767px) {
  #top #header,
  #top .header_bg {
    height: 210px !important;
    max-height: 210px !important;
  }
  .responsive #top #wrap_all #main {
    padding-top: 210px !important;
    border-bottom: 3px solid #000
  }
  #top .logo .widget {
    align-items: center;
  }
}