Clarification to avoid confusion :
"I'm puzzled as to whether the contraflow nature of cycle lane in Nevada Street is correctly represented." ........ etc

I'm puzzled as to whether the contraflow nature of cycle is correctly represented. Komoot seems unaware of it (routing westbound riders via King William St). It may be that Komoot is using an an out-dated version of OSM. But its worth checking the tags for the cycle lane to make sure its shown as westbound contraflow .