The servers responsible for continuously re-drawing the map on openstreetmap.org are quite overloaded for the Europe area. Hence, it can often take a bit of time before the map is redrawn after an object (such as a path) is added or changed. Your browser might also have cached the map in an older state. You can refresh your cache by forcing a refresh. E.g. Ctrl+F5 in chrome on Windows. See if that works.

Also keep in mind that different 3rd party consumers of OSM data have different refresh times. E.g. for Strava it can take a week easily before a path becomes visible there.

If you enjoy hiking and you use OSM for that (directly or indirectly), adding paths that you know of can be quite a rewarding experience. That's how I got into contributing to OSM.