In BBEdit it is called Secondary custom highlight color. The color you choose does not dim for the search window. And even behind the Terminal it does not dim. If I deactivate it, I get the same grey as in Drafts.
I have found a workaround see https://forums.getdrafts.com/t/can-you-change-the-colour-of-of-the-marking-you-get-on-a-search-hit/14987/4 still nice to have the opportunity to edit the colour.