Hi @mueschel,
I use the "cycleway:right:lane_markings" tag to indicate if the lanes on the bike lane are separated by a lane marking. It is a two way bike lane on one side and some parts of it do not have lane markings and some do. I am not sure what "cycleway:right:marking" is used for because I can't find anything on overpass turbo (or maybe I am not looking correctly). Two way bike lane on one side is already quite a rare thing so maybe no one has ever bothered to tag whether it has lane markings so this could be a first. Hope this helps.