Search all paroduct titles, categories & taxonomies with one search field

Hi there. I have a simple search field in my header to search through my universities (products) by keyword. I would like this field to search for the keyword across all categories & taxonomies, but it seems to be only searching the post titles and descriptions.

I have 94 products in United Kingdom, but if I search “United Kingdom” in my header search bar, it only comes up with 2 results.

here is a page that contains the header search bar:
https://www.ieabroad.com/institution/city-university-of-london/

The page I need help with: [log in to see the link]