Insert picture in Mobile Menu

Well on Menu ( Dashboard – Appearance – Menus ) you can

add an additional home link.
you can add html code to the “Navigation Label” of that menu-item.

do you know how to make those extra infos visible on menu options?
There is a flyout menu on top “Screen Options” mark css-classes too!
on each menu-item there is a little arrow on the right:

insert in navigation label the html vor your logo
f.e.
<img src="/wp-content/uploads/logo.png" /> maybe an absolute path is necessary
give to that menu item a custom-class: only-burger

now – to see the doubled Home-Menu-item Link only on hamburger:

#avia-menu .only-burger.menu-item {
    display: none;
}

so this image is the first list item on your hamburger – and has direct link to home. – bingo