Why does OpenStreetMap think the road to the roundabout is one-way (in the wrong direction) and not route along it? Here is an example route where it incorrectly routes around the block:
I tried removing the road to the roundabout and putting it back to see if that would somehow fix it, but it still won’t navigate along the road. Changeset here:
You need to wait at least 2-3 days for the data to update for that specific routing engine, and it is likely not different for the other options. See at the bottom of About routing.openstreetmap.de
As to why the routing link that you shared is not working, I tried the “Reverse direction” button and that was not working also so oneway is not the problem. Then I tried another router that I know updates the routing data every 24 hour and that routes fine. Then saw you can also select other routers in the link you shared and I see also no problem with GraphHopper.
So the problem seems to be with OSRM, it could be that the data is too old, it could be there is another problem.