I've anyways only looked at bike routing: https://www.openstreetmap.org/directions?engine=fossgis_valhalla_bicycle&route=46.5258%2C6.5621137%3B46.5227814%2C6.5174317#map=18/46.523078/6.516700 and must have copy-pasted the wrong URL.

All three routers are wrong in car mode: https://www.openstreetmap.org/directions?engine=graphhopper_car&route=46.5258%2C6.5621137%3B46.5227814%2C6.5174317 as you say. I hope that the addition of the highway=service helps (in some days)