I am an end user of OSM data, utilising it with a bunch of popular GIS programs and I would say that if only possible, just draw the cycleway as a separate way and don’t start to fiddle with left/right/east/west/opposite or the like. I believe it is better for OSM data too because then you can give also attributes for the cycleway (surcafe, restrictions etc.). But there are for sure other and as good opinions than mine.