In order to add the extra elements or changing it’s layout for the mobile without effecting the Desktop menu requires to do the custom code in your theme file. Could you please share the details along with the store url and collab code so that I can send you request for accessing the store and do the requested changes.
Thanks
You may also rearrange or hide elements in the Horizon theme mobile menu via CSS media queries like @media (max-width: 768px). Add new items by editing the mobile menú liquid file and adding the new links but within a mobile specific condition so your desktop won’t be modified.