How to disable individual elements when displaying WooCommerce products on a separate page and in the menu?

Question

WordPress

Good day!
Please help.
Short codes display certain WooCommerce products on the main page and in the mega menu. But the fact is that along with the image of the product with a quick view, its name, and price, the categories of these products and the "compare" button are also pulled up here (displayed). That is, everything is exactly the same as in the archive of goods.
Question. How can the latter (category display and "compare" button) be disabled everywhere except for Woo archives?
In the archives, this looks informative and appropriate, but in the menu and somewhere on a separate page, such a product already seems like a cumbersome block. And .. (I'm an amateur) apparently this, in this case, still significantly increases the number of DOM elements.
Thank you.