What you’re looking to do is quite complex.
First of all, it is not possible to directly order posts by a term. What you need to do is to get all of the terms, loop through the terms and get all of the posts in each term based on the list of links on the page.
get posts using "post__in" query where the post_in value is derived from the list of links
if there are posts in the category
get the category image and display
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