Show the Preorder button and badge in the "Related products" section on product pages

The problem
Preorder products show the Preorder button and badge on my home, collection and search pages, but not in the "Related products" section on individual product pages. There, preorder products still show the theme's regular "Add to cart" button and no badge, so customers can't tell the item is a preorder until they click through.

Example
On https://staticatx.com/products/the-tear-garden-the-brown-acid-caveat-tangerine, the related products include Delerium – Karma. It's an active preorder but shows "Add to cart" with no badge.

What I'd like
A page placement for product recommendations on product pages, alongside the existing Home, Collection and Search options under Preorders > Settings > Pages. Ideally it would also cover the search dropdown suggestions and Quick Buy popups, so preorders look the same everywhere a product card appears.

Why it matters
Related products is one of the main ways shoppers move between products. A preorder shown as "Add to cart" there sets the wrong expectation about when the item ships.

My setup
Store: staticatx.com (7d90ee-b2.myshopify.com)
Theme: Maranello 5.4.0
The related products cards use the same product card as my collection pages, loaded into the theme's product recommendations section after the page loads.