It’s all already there. What do you mean by “cannot see your track in OSM”? Maybe in the default view you couldn’t see it, because it wasn’t rendered yet.
Why is this path so jagged? Did you turn a GPS trace directly into an OSM way? If you do this, you should edit the way by hand to smooth out the GPS inaccuracies.
I can see you put hiking route tags directly to that path. You should rather create a route relation (with route tagging) and add your path(s) and other ways into that relation. More in the OSM Wiki.
and on the main openstreetmap.org view you can switch on the so called data layer to really see all elements, even when they are not displayed by the rendering stile of OSM’s mapnik tile graphics)
AND: your hiking tracks have many many nodes! before uploading via JOSM to the main OSM database server, try to reduce the number of nodes by selecting your newly created way and choose Simplify way (Shift-Y) … so that superfluous nodes are deleted.
And when watching that area with your new ways on osm.org, try to refresh broswer cache via F5 or shift-F5 … visible now?
Regarding hiking tracks, what do you think is better among ways and relations, considering rendering and tags additional informations?
I did not find uniqueness of point of views.
Many tags that I’ve used seems to be appliable to both ways and relations…