can you have default search engines in address bar and the added search bar

Using version 152.0.1 on windows 11. Have added an extra 'search' box as described in 'Add the Search bar to your Firefox toolbar ". Is it possible to have a default search engine i.e. Google (and the option to choose other engines) on the big search / address bar, but have a DIFFERENT and ONLY option to search with one i.e Wikipedia engine on the smaller search box? i.e. one general search/ address box, and one if you know you want to search with a different default search engine. Tried everything google AI suggested and nothing worked; it said both boxes are 'linked'. Thanks.