How to search CPT’s by meta query from the admin dashboard?

You can install the Query Monitor plugin to see what actual query that is being executed when you perform a search.

I suspect the problem you are having is that you are not unsetting the initial query vars. You are adding the meta query, but you haven’t removed the s= parameter, which only searches for your keyword in the title, content and excerpt.

Below $query->set('meta_query', $meta_query);, try adding either of these: $query->set('s', ''); to set ‘s’ to an empty string or $query->__unset('s'); to unset it.