the problem is that MNF does not give proper routing instructions while osm seems to be ok. Neither it is perfect - maybe it is possible to give instructions like: "use footway"
I would not consider such situations as a routing bug.
Those are tracks designated to pedestrians and bycicles parallel to the main street. This is basically part of the same street and just separated in OSM data. To take the path designated for bicylces on a street is not a question of routing but to keep your eyes open and use that part of the street in reality.
I do not understand what you mean. If I calculate a bicycle route it does lead me perfectly over the cycle path.
And of course it should not tell you to turn right. The cycle path does belong to way just like the sidewalk. Oldie mentions that it "is basically part of the same street".
It's much more then that: It is legally part of the same road: (multi-lane separated) road and/or (separated) cycle lanes and/or (separated) sidewalks.
So you literally stay on the same road and simply go straight on using the exact same road, even though you think there is a little curve.
If you were in a car and there was a slight curve in the road, or such a traffic slowing bottleneck at schools or so, you simply would't want to hear to bear right, or something alike.
I was wondering why it says "turn right" instead of "bear right" while it is (in my opinion) exactly the same situation. n this situation iIt would be best to let the navigator just say nothing (but it is nearly impossible to recognize which way is just multi-lane separated and ehich one is independent - I know this).