personally, i am not in favor of this change (perhaps @featheredtoast might feel differently) because the whole idea is to be consistent with desktop view and have it before the logo. however, if you need it, then you can just add this css in another theme component on your forum to override the order of items.
.d-header {
display: grid;
grid-template-areas: 'logo left-menu custom-header-icon-link-1 custom-header-icon-link-2 custom-header-icon-link-3 custom-header-icon-link-4 custom-header-icon-link-5 extra-info chat header-buttons search right-menu'!important;
}
result:
the burger icon should not show in the scrolled header on mobile in order to maximize the header space for longer topic titles