Front End Search Settings : Find & Display Taxonomy terms with Ajax

Hello, Ernest,

In the section :
Front End Search Settings > Categories & Taxonomy terms.
I have a type of taxonomy with thousands of terms (these are ingredients for recipes).

If I choose to filter my search results by ingredients terms with the option “multiselect with search” all the list of ingredients is populated and added to the page, which makes the loading of the page much much heavier and the loading speed is much longer for everydoby.
I can keep this function on a specific page of the site but unfortunately not on all the pages because not all the visitors of a page systematically use the search function.
However, it is important for us to offer this option of filtering by ingredients everywhere.

Would it be possible to have a search in ajax to return only the terms corresponding to what is searched in this filter?

Thanks a lot ?