The implementation of T294932: Lists: Auto-complete/lookahead search for adding tools is using a simple_query_string full text search that only really differs from the site search implementation in the fields scanned for matches and lack of computed facets.
We may get both better performance and more exhaustive matching by making some changes to our toolinfo document mapping to add specially typed subfields to name and title and also changing the query type to something like multi_match using N-gram tokenizers (one with shingle size 2 and another with shingle size 3). N-gram searches end up working a bit like a double wildcard search (*something*) but are more runtime performant at a cost of larger indexes.