I would stay away from the wp_nav-Menu function as it will be too hard to customize the HTML, but instead go for a more data friendly function like:
Use this to get you menu (or a similar function you find), and then loop through the items. Each taxonomy item will have a taxonomy and a term_id. You can use these pieces of data to construct the $post_id needed to load data from the term!
You can load how to load data from the term from this doc:
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