Search field (the one you see when starting entering text into Near location, same in routing) links bookmarks and addresses. They both are searched while you type (assuming that provider supports it).
In many of my replies I mention provider. From the beginning, Pure Maps (with its earlier names Poor Maps and WhoGo Maps) was designed to be modular. It is easy to add new providers for search, nearby venues, and routing.
Each provider can have it's own settings that alter the action. For routing, some search only routes for cars, some do more. For nearby venues, default online provider is https://foursquare.com/. That "Best" or Most Popular comes from them.
Over offline provider - OSM Scout Server - I have some control as I am the author of it. But note that even there, routing is provided via one of the libraries - Valhalla - and the server can be considered as just an extra layer for that. For search (global and nearby), though, control is larger as it is using geocoder-nlp that I wrote. Although, it becomes question of my time and priorities among projects that I contribute to.