The build-in cycling routing engines don't give a strange loop, e.g.
https://www.openstreetmap.org/directions?engine=graphhopper_bicycle&route=52.05275%2C4.38280%3B52.05274%2C4.38491#map=19/52.05257/4.38385

There doesn't seem to be a problem with the Openstreetmap database. The way https://www.openstreetmap.org/way/129890484 is tagged as a cycleway, which is correct.

Probably there is a bug in the app you are using?