OSM main page has a button “route” (german) which shows actually 3 different routers. Is it possible to extend this list? If yes, how it is performed? If admins only, can it be extended by “https://cycle.travel/map”?
It can be extended, but as the person who runs cycle.travel, I wouldn’t permit it to be on there - I don’t have the time or resources to administer a routing server for visitors to osm.org and there’d be no practical way for me to recoup the money it cost. You can use cycle.travel’s routing at cycle.travel itself.