Show burger menu to the left of the centered logo

real mobile devices do not have a shrinking header! – i do not see your conversation on private content area – and i do not see your site – but if you got css rules with classes like header-scrolled – this will not work on mobile devices!
See line 81 in avia-snippet-sticky-header.js :

if( shrinking && ! isMobile ){

As I said, as a participant I cannot see your private message area, so I cannot see a link if it has been posted. The link would be necessary for verification – because a screenshot is not meaningful enough to give advice.

if that is your css – the

@media only screen and (max-width: 768px) {

is nested with a nother media query.
your :

    @media only screen and (max-width:767px) {
        .responsive #top #header_main > .container .main_menu .av-main-nav > li > a {
            padding-left: 0;
        }
    }

is inside another media query ( with the same settings )

next hint: use for the max-width media query the odd setting – and for min-width the even ones.

I don’t know if the above leads to conflicts, but put this as code instead:

@media only screen and (max-width: 767px) {
    /* Add your Mobile Styles here */
    .responsive #header_main_alternate {
        display: block;
    }

    .responsive #top #header .main_menu {
        width: auto !important;
    }

    #header_meta .phone-info-custom::before {
        background-color: #ffffff !important;
    }
    .responsive #top #wrap_all .main_menu {
        left: 0px !important;
    }
    .responsive #top .logo {
        width: 50% !important;
    }

    .responsive #top #wrap_all .container {
        float: right !important;
    }

    #header_meta .phone-info-custom {
        font-size: 15px;
        font-weight: 800;
        color: #000000;
        padding-top: 70px;
    }
    #header_meta .container {
        max-width: 50% ;
        margin-left: 0px;
        margin-right: 0px !important;
        padding-left: 0px !important;
        padding-right: 0px !important;
    }

    /*PHONE INFO*/
    #header_meta .phone-info-custom::before {
        display: none !important;
    }
    .phone-info {
        padding-top: 5px !important;
    }

    /*LOGO*/
    .responsive .logo img {
        float: right !important;
    }

    .responsive #top .logo {
        position: static;
        display: table;
        height: 80px!important;
        float: none;
        padding: 0;
        border: none;
        width: 95%;
    }
    .main_menu {
        margin-left: 0px !important;
    }
    a {
        padding-left: 0px !important;
    }

    .responsive #top #header_main > .container .main_menu .av-main-nav > li > a {
        padding-left: 0;
    }
}

/* 💻 TABLETTE (entre 769px et 1024px) */
@media only screen and (min-width:768px) and (max-width:989px) {
    .responsive #top #wrap_all .av_mobile_menu_tablet .main_menu {
        left: 0 !important;
    }
}