But if I choose to download a png from this view (or pdf or svg) it shows everything :
On some zoom levels it shows the whole path, on the others not (or even nothing)… Could you tell me how long it will take before openstreemap view shows everything on every zoom levels ?
Depending on the “layer” used, from minutes to about a week.
Sometimes large area maps may be delayed quite a long time, if something is going wrong, or there is some special processing happening.
Often the tile is updated immediately, but your browser or ISP is caching the old tile. In particular, because web sites fail to give accurate information on how long to cache pages, but images don’t change often, and can be large, on most web sites, ISPs will often apply a rule that will keep stale versions for images for a long time.
Zoom level 15, and, I think, 14, are generated on the fly for the standard “layer”. any delay in updating those is due to intermediate caches.
The path will not show on some zoom levels, anyway, as the level of detail depends on the zoom level.
You can force the OSM server to regenerate a tile immediately, but this is not something that people should be in the habit of doing.