Routes, waypoints and tracks are all stored in .gpx files on newer devices like yours. But there are many files, I believe it creates a new waypoint file for each day you use the device for example.
Basecamp should be able to figure all of this out I think. Honestly, I don't use it much myself these days. But IIRC, you can create a new list in Basecamp and then import all of your user data from thje 62st to it. You can then use the filter feature to separate waypoints, tracks and routes.
To use the data in another program, you could just create another list, drag whatever data you want to it, then export as a .gpx file.