A trail can be clearly visible on the map and still not be routable. The reason explains most surprises about offline use.
What you see is map tiles: pictures, drawn by a map service, cached as you pan around. They make the map look right, including with no connection.
What routing uses is OpenStreetMap data: the actual paths, junctions and route relations behind that picture. It records which way connects to which, whether a way is a track or a staircase, and which waymarked route it belongs to. That is a separate download, held in its own cache.
So a picture of a path is just a picture. Until the underlying data for that area has been downloaded, TrailRunner Mini cannot route along the path, cannot show its waymark shield, and cannot offer it under Prefer Trails.
All three are the same thing: tiles present, data absent.
Frame the area you care about and choose Map › Preload Visible Region. It downloads what is missing for that area and leaves what you already have alone. Once it finishes, routing, waymark shields and trail selection all work there, with no connection at all.
Tip: preload before you leave. Preloading is per area, so do it deliberately for the region you are heading to rather than hoping you panned across it.
OpenStreetMap is edited constantly. New paths appear and closures get mapped. Downloaded data is refreshed periodically on its own, and you can force it now. Map › Refresh Region revalidates the visible area against OpenStreetMap and folds in what changed, keeping everything else. Do this before a trip to an area you preloaded a while ago.
Map › Clear Map Cache throws all of it away and reports the space freed. Nothing is lost permanently, but you lose the offline coverage you built up. Prefer Refresh Region unless you want the space back.