Logo in the middle and burger menu on the right in desktop mode

if you have : logo center, menu below
and : menu show as burger always
and : show search in menu
then we are nearby:

after that : you can see on my test-page for that: https://webers-testseite.de/cynthia/
a little quick css:

@media only screen and (min-width: 990px) {
  .html_header_top.html_logo_center #header_main_alternate .main_menu #avia-menu {
      display: inline-flex !important;
      width: 100%;
      flex-flow: row nowrap;
      justify-content: space-between;
  }

  .html_header_top #top .av_header_stretch .container.av-logo-container {
    width: 60%;
    z-index: 101;
  }

  #header_main_alternate {
    margin-top: -60px;
    border: none;
    position: relative;
    min-height: 58px;
  }
  
  .html_header_top.html_header_sticky.html_large.html_bottom_nav_header #main {
    padding-top: 116px;
   }
}

@media only screen and (max-width: 989px) { 
  .responsive.html_header_top #top .av_header_stretch .container .inner-container .logo {
    width: 50% !important;
    z-index: 101;
    position: relative;
    left: 50%;
    transform: translateX(-50%);
  }
  .main_menu {
    width: 100% !important;
  }
  .av-main-nav-wrap {
    width: 100% !important;
  }
  .av-main-nav-wrap > ul {
    display: inline-flex !important;
    width: 100% !important;
    flex-flow: row nowrap;
    justify-content: space-between;
  }
  .responsive #top #wrap_all #header .container {
    width: 95% !important;
    max-width: 95% !important;
  }
}

If you like to have the burger symbol on the left and the search on the right you only had to change the flex-flow to:
flex-flow: row-reverse nowrap;

if you like to have the burger slide out from the left then – please do a search this is often asked.

see now: https://webers-testseite.de/cynthia/

By the way working on that – i recognized that it might be more easy to use the normal header style: logo: left – menu right !