This is reminiscent of the rule of the road, but for an individual path and dependent on the mode of transportation. driving_side=left/right is well-established for indicating the rule of the road that applies to a given road or all the roads in a region. This key affects some aspects of routing in OSRM and rendering in OSM2World. Despite the key’s name, it applies to any traffic that uses the main carriageway in the normal fashion – not necessarily traffic that has to hug the shoulder, as pedestrians do. The sides are relative to the centerline and have nothing to do with the position of the steering wheel.
Given that the segregated=yes line is essentially a centerline, what if we extend this tagging scheme with walking_side=left/right and cycling_side=left/right? This would make it possible to assign each mode of transportation to one side or the other without getting into lane-level detail, which is complementary. I realize the analogy has its limits: if you’re allowed to bike on the left, then you can bike in either direction. But I’d appreciate the simplicity of saying just a side and not having to fuss over any notion of priority or hierarchy among the modes of transportation.