Can you share the page password?
I can't see in the partial CSS you've shared that you're hiding the categories on mobile, but in looking at another page you are hiding it for the boxes page, looks like this:
@media screen and (max-width: 575px)
.products.collection-content-wrapper .nested-category-tree-wrapper {
display: none;
}
You could target this to just the boxes page, or even hide it on desktop as well as it currently serves no purpose. Targeting to just the boxes page will allow it to show up on mobile on the pick'n'mix page, and if you need help styling it let me know.