Grouped products are not identified as such in "Search Products"

Variation products are identified with the suffix “with X”. But grouped products are not identified at all.

In the WC products page the identification works like this:

Striped Tie < Black suit
Black Shoes < Black suit
Gold Watch < Black suit
Tie < White suit
Black Shoes < White suit
Silver Watch < White suit

The problem here is adding “Black Shoes” to a bundle. The “Search Products” module lists the products like this:

Striped Tie
Black Shoes
Gold Watch
Tie
Black Shoes
Silver Watch

https://www.ads-software.com/plugins/wc-product-bundles/