Check out this link.
Heaps of options, and it does mention open source options. All will use OpenStreetMaps as the map and routing.
The Maps.Me solution looks pretty good - https://wiki.openstreetmap.org/wiki/MAPS.ME
Navit seems to be more focused on in-car navigation, which might be more suitable depending upon ...
OsmAnd is a GPS app and famous as offline navigation app.
However, it has also the tracking features, so you load GPX track files, follow and track you activity, besides having some stats about the activity.
It is opensource and it has not 3rd party online trackers or SOCIAL sharing. You can download/install from Play and F-Droid