Here is the promised summary report:

1. The SQL (.db) files contain two relevant tables: 'trails' (listing the 'Named Trails') and 'trail_segs' (listing the trail segments for these trails).

2. The table 'trail_segs' defines segments of the 'Named Trails' by endpoints given in Garmin binary coordinates.

3. The routing algorithms follow trail polylines between the segment endpoints and assemble the 'Named Trails' from the trail segments.

This may sound simple now.
However, it was quite an effort to find out how it works.
The essential discoveries were made by merlinboy.