Resolve a free-text query to the longest catalog brand + model, returning the leftover text as a title keyword.

Used by the smart-search box when the user presses Enter WITHOUT picking a suggestion: the frontend applies brand_id + model_id as filters and pushes the residual ("the version part") into the free-text query keyword search. Versions are intentionally NOT resolved — their strings are too inconsistent across the 93 sources to match exactly, so the trailing trim text is matched against car_listings.title instead.