categories relevant to search results

Hi, I have a suggestion.
When searching for anything, for example, "car," it shows the results that match the search, but all the categories in the sidebar are displayed. It would be better if it updated and only showed the categories that have a match with the search, since it doesn't make sense to show, for example, the "real estate" category if the user is searching for "cars."

Ideally: When the user searches for "cars," the sidebar displays, for example, the "vehicles" and "toys" categories for toy car listings. The list of categories should update in real time depending on the user's search.
Thanks.

you would need to decide if you search by listing text or category text.
what could make sense to include into search also category name at start, but no idea how it would affect relevancy of search.